NDSolve throws Dot::dotsh error

Question

First, NDSolve is an incredible tool. I've been pushing it hard. Second, this error arises because I don't fully understand how best to handle the singularities. Third, I share this because

1. This throws a Dot::dotsh error on step 90 and then brings down the kernel. Not a graceful exit
2. The behavior is similar to that discussed in FEM Mesh related errors that proved to be a bug

Has anyone seen similar behavior? Have a workaround?

Background: Using NDSolve to adjust

1. the constants cee[i][t] defining the functions g[x,i,t]
2. the integrals of g[x,i,t]
3. constants F[i][t] -- the optimality criteria are in terms of F[i][t]+G[x,i,t]
4. the points s[i,j][t] where the functions g cross

in order to obtain certain optimality criteria.

Singularities: Arise when g[x,i,t] and g[x,i+1,t] are tangent at a single point. To avoid these, when the points s[i,i+t][t] and s[i+1,i][t] get too close, I try to adjust the derivatives to keep them from moving closer using "slacks". This works well when one or two function pairs are getting close to being tangent. As you can see in the figure, this is a case where several curves are becoming tangent. Would welcome any suggestions for managing this sort of phenomenon more elegantly and robustly.

Here's code that produces the issue (on Mathematica 12.2.0.0 on Mac). It works fine up to step 89. Step 90 brings down the kernel. Apologies for all the definitions at the beginning and the awkward translations. They capture the results of several previous steps to get to this point.

With[{params = {sigma->1.`80.,h->1.`80.,p->-1.`80.,U->2.`80.,M->2.`80.,theta->1.`80.,kplus->0,kminus->0,kvplus->0.01`80.,kvminus->0.01`80.},
      rates = {u[1]->-10.`80.,u[2]->-6.`80.,u[3]->-1.`80.,u[4]->1.`80.,u[5]->3.`80.,u[6]->4.`80.,u[7]->5.`80.,u[8]->6.`80.,u[9]->8.`80.,u[10]->10.`80.},
      kays = {k[1,1]->0,k[1,2]->0.000948802000000000000413946654731489616096951067447662353515625`80.,k[1,3]->0.00319882000000000000540512079538757461705245077610015869140625`80.,k[1,4]->0.001861119999999999961859398212027372210286557674407958984375`80.,k[1,5]->0.0043391096400000000071726382298853419428041888750158250331878662109375`80.,k[1,6]->4.8726399999999999885515709896477432039318955503404140472412109375`80.*^-6,k[1,7]->0.0012894856399999999875156399785358640741605995572172105312347412109375`80.,k[1,8]->0.001244516999999999997371380455746248117065988481044769287109375`80.,k[1,9]->0.000494853999999999975313580424796100487583316862583160400390625`80.,k[1,10]->0.0022131436400000000402874824299848111053279353654943406581878662109375`80.,k[2,1]->0.00473396800000000007348222030856277342536486685276031494140625`80.,k[2,2]->0,k[2,3]->0.0036933234000000001741835509161404615952051244676113128662109375`80.,k[2,4]->0.003059352999999999898894653682646094239316880702972412109375`80.,k[2,5]->0.003959572999999999977187303823455977180856280028820037841796875`80.,k[2,6]->0.0000545933999999999980921872033690078751533292233943939208984375`80.,k[2,7]->0.00090994899999999995753030557210649931221269071102142333984375`80.,k[2,8]->0.00029571499999999999695743380101475850096903741359710693359375`80.,k[2,9]->0.0010991830000000001044124786631073220632970333099365234375`80.,k[2,10]->0.001833607000000000010302148023555446343380026519298553466796875`80.,k[3,1]->0.00506821399999999970542585714383676531724631786346435546875`80.,k[3,2]->0.002353580000000000081727957734756273566745221614837646484375`80.,k[3,3]->0,k[3,4]->0.0039197689999999995973112287828143962542526423931121826171875`80.,k[3,5]->0.004931654999999999957997764976624921473558060824871063232421875`80.,k[3,6]->0.00059741799999999995081367831772922727395780384540557861328125`80.,k[3,7]->0.00188203099999999993834076672527544360491447150707244873046875`80.,k[3,8]->0.00264929500000000007868539153577103206771425902843475341796875`80.,k[3,9]->0.0019595989999999998028290537632756240782327950000762939453125`80.,k[3,10]->0.002805688999999999991112609176724390636081807315349578857421875`80.,k[4,1]->0.004469362000000000161026303402422854560427367687225341796875`80.,k[4,2]->0.00183009100000000005277478454246420369599945843219757080078125`80.,k[4,3]->0.00133770000000000004354572258336020240676589310169219970703125`80.,k[4,4]->0,k[4,5]->0.003694967000000000064731386917316058315918780863285064697265625`80.,k[4,6]->0.000191704000000000006342926184288444346748292446136474609375`80.,k[4,7]->0.0006453430000000000450743886659665804472751915454864501953125`80.,k[4,8]->0.002125806000000000049732218343478962196968495845794677734375`80.,k[4,9]->0.002895108999999999876973078016817453317344188690185546875`80.,k[4,10]->0.001569001000000000097846231117415527478442527353763580322265625`80.,k[5,1]->0.004310083000000000143236977834249046281911432743072509765625`80.,k[5,2]->0.00380053999999999990249376080608811889760545454919338226318359375`80.,k[5,3]->0.00353179899999999982718699997885636321370839141309261322021484375`80.,k[5,4]->0.00219409899999999978364127739549616080694249831140041351318359375`80.,k[5,5]->0,k[5,6]->0.00171352699999999992671283199907605876433080993592739105224609375`80.,k[5,7]->0.00283944199999999982871566606146274125421768985688686370849609375`80.,k[5,8]->0.00409625499999999989945119460710287739857449196279048919677734375`80.,k[5,9]->0.00023392899999999998915910237595738863092265091836452484130859375`80.,k[5,10]->0.00376309999999999988148750851291168828538502566516399383544921875`80.,k[6,1]->0.004771982000000000133377309197157956077717244625091552734375`80.,k[6,2]->0.0022137440000000001283364525761498953215777873992919921875`80.,k[6,3]->0.0036387300000000001760913637127714537200517952442169189453125`80.,k[6,4]->0.0046635749999999996651123268520677811466157436370849609375`80.,k[6,5]->0.004334237000000000007184086658895694199600256979465484619140625`80.,k[6,6]->0,k[6,7]->0.0012846129999999999875270884075462163309566676616668701171875`80.,k[6,8]->0.00250945900000000012529388637716465382254682481288909912109375`80.,k[6,9]->0.002703404999999999870630151832529008970595896244049072265625`80.,k[6,10]->0.002208271000000000040298930858995163362124003469944000244140625`80.,k[7,1]->0.0038240190000000001159519147364562741131521761417388916015625`80.,k[7,2]->0.004772821000000000116365861391187763729249127209186553955078125`80.,k[7,3]->0.0064269710000000000726938509387764497660100460052490234375`80.,k[7,4]->0.00524372299999999980329827564684563867558608762919902801513671875`80.,k[7,5]->0.003049624000000000019656998251349477868643589317798614501953125`80.,k[7,6]->0.0038288916400000001159404663074459218563561080372892320156097412109375`80.,k[7,7]->0,k[7,8]->0.005068536000000000113323295192202522230218164622783660888671875`80.,k[7,9]->0.00328355300000000000881610062730686649956624023616313934326171875`80.,k[7,10]->0.000923658000000000052771842451448947031167335808277130126953125`80.,k[8,1]->0.00566556300000000019612134138924375292845070362091064453125`80.,k[8,2]->0.0055891789999999996751967046293430030345916748046875`80.,k[8,3]->0.0065510550000000000725464133211062289774417877197265625`80.,k[8,4]->0.005927627999999999890146096248599860700778663158416748046875`80.,k[8,5]->0.00650640799999999998315391991354772471822798252105712890625`80.,k[8,6]->0.0056437723999999996732888918327120109097450040280818939208984375`80.,k[8,7]->0.0037648000000000000041244785364824565476737916469573974609375`80.,k[8,8]->0,k[8,9]->0.005210860000000000318010062727580589125864207744598388671875`80.,k[8,10]->0.004688458000000000056896320987931403578841127455234527587890625`80.,k[9,1]->0.005312981999999999947748019479831782518886029720306396484375`80.,k[9,2]->0.003566610999999999913334658430130730266682803630828857421875`80.,k[9,3]->0.00329786999999999983802789760289897458278574049472808837890625`80.,k[9,4]->0.001960169999999999794482175019538772176019847393035888671875`80.,k[9,5]->0.005655136999999999859213561936854830491938628256320953369140625`80.,k[9,6]->0.0014795979999999999375537296231186701334081590175628662109375`80.,k[9,7]->0.0026055129999999998395565636855053526232950389385223388671875`80.,k[9,8]->0.00386232599999999991029209223114548876765184104442596435546875`80.,k[9,9]->0,k[9,10]->0.003529170999999999892328406136954299654462374746799468994140625`80.,k[10,1]->0.0037746849999999998459543348872102797031402587890625`80.,k[10,2]->0.004723486999999999846368281541941769319237209856510162353515625`80.,k[10,3]->0.00565776499999999979407215577875689405118464492261409759521484375`80.,k[10,4]->0.00432006499999999975052643319539669164441875182092189788818359375`80.,k[10,5]->0.002125965999999999966885155799900530837476253509521484375`80.,k[10,6]->0.0037795576399999998459428864581999274463441906846128404140472412109375`80.,k[10,7]->0.004285693000000000141280764864859520457684993743896484375`80.,k[10,8]->0.005019201999999999843325715342956527820206247270107269287109375`80.,k[10,9]->0.00235989499999999995604425817585791946839890442788600921630859375`80.,k[10,10]->0},
      imin = 4, imax = 9, 
      beta = <|4->9,5->8,6->8,7->9,8->9,9->9|>, 
      tau = <|4->4,5->4,6->4,7->4,8->4,9->4|>,
      transient = {5,6,7,8}, recurrent = {4,9}, 
      badedge = 4\[DirectedEdge]9, ifix=4,
      sol = {cee[4][t]->-3.302791794819281596993754918490030955226349847121628160661343999062238531610238268496173916025507`78.53558590114208,F[4][t]->0,cee[5][t]->-2.01015278250513775193133051684584753505335423622868961961597414581628527876419169133487159325893`78.0817234313792,F[5][t]->1.343401625712991005406165202250305478094435346189466654599143491341899843261523924856541322142774`78.70546098109291,cee[6][t]->-2.158841423817423445929021697444016615740714802618823197582128636785997746489392370814433861513868`77.95959345812315,F[6][t]->1.427794232532325113002858236024552635056297644849789538816171896112257114351069513634824655343978`78.68984088472966,cee[7][t]->-2.494275023500774311383478819031971217608964889260843826746008836891013231220354764454279694105394`78.63841490082763,F[7][t]->1.469964728191305670104144114920602124613752751536596529895854311670222685243435572198114948124104`78.60625348577585,cee[8][t]->-2.659312902881342888249272958154388089334496177803768287020470186306008806717256525821592811147189`77.78647627276752,F[8][t]->1.497336648672494286294019352619040523337514273218063215390475941700163688623663205919466704233362`78.67386581427606,cee[9][t]->-3.251185532877928483265430755630707901347888595847215401235340823103658834871238823453578979885777`79.46228914704172,F[9][t]->1.521206236469674296705328412178746857709956387567120650707190578072839578102620759279284377440764`78.65105506897532,t->1.946984263023427866123446045045663210783108766777723209882726584829270678969910587628631839086304`80.},
      gamma = 1.946984263023427604549523495604794227616510386383352725147800943701679274630699882935658645126065`80.,
      eps = 0.002467497495021921118119563337708397058411989621746925309331579003232261728963181038287124459513`75.11118243564009,
      svals = {s[4,4][t]->0,s[4,5][t]->0.190087865187306079347774896944024078764595727983799391707412558900002483159768065236175053796497`78.12734067841095,s[4,6][t]->0.190067511329536623998513482119111640681151098400723852917252029540230430519101532677398385832233`78.1291965639342,s[4,7][t]->0.190066961592769588081767703584330154900311951719778210086657593386671735567878944153018479360661`75.58177481037254,s[4,8][t]->0.135521322674871638057978680200200464316895565454473961450419677785130780219380120968639399757355`77.990594202613,s[4,9][t]->0.111897221571789500885116511377590879608647841143903077876360533775999498301945608697126784130255`77.90185067358271,s[5,4][t]->0.190860463182425692050716361677237478423649971832608508871918252181955418107288039741305468646195`78.13562084908294,s[5,5][t]->0,s[5,6][t]->0.190029588032196751065027751763413656389324723815287711272867047478318513834938101347622647467904`78.13203667868355,s[5,7][t]->0.190047079006321721760470939696033101678163552198939570166711545085338396622182597487360025738304`75.30221419722788,s[5,8][t]->0.118826532001887559772871320360363732063964257914701255184653799067801726444121035491640196624339`77.9352850479685,s[5,9][t]->0.096690102007063943634636937686381599194589253454058235270560436777569213758930409799338167637506`77.69491729152642,s[6,4][t]->0.190880546308302371759876712501604430048923251166091491269676563343668167001066455555354740521756`78.13477020581733,s[6,5][t]->0.190917992258709403401558203630710799540871029042871087091734547460147664299037083952524240128583`78.13291770883845,s[6,6][t]->0,s[6,7][t]->0.190065316813216850497599693136618771548435777370231490966921596640344373217447308135324361224472`74.98728997313931,s[6,8][t]->0.101163979611307745143096480101771676336768704042898647500785657574296787146064140507816131423978`77.86728823527966,s[6,9][t]->0.084357124225972292197652946909845137560331165156490839393532658051364362301501622265315934406331`77.54191796970049,s[7,4][t]->0.190880873630853732049595609368503542631507821912291426095320191070317152211301774782582689681218`75.58333963097162,s[7,5][t]->0.190900306767741811327364976559911153438199285533937483735457018189088522169830133739416578180947`75.30459181724046,s[7,6][t]->0.190881854019862246866455459172735379616245945484751774337619204686585105730381173515450490140969`74.98992804400359,s[7,7][t]->0,s[7,8][t]->0.057202224888746466696356719376470990596468816875733018193199701708565877341357433828830192201796`76.67575320659363,s[7,9][t]->0.065065748977569297991850050136490076550902655509932021238590421349533413535631772281482360891249`78.09375472812498,s[8,4][t]->0.229813367114266495299805593208395472535241317355907796274512817116168943978612770077192813349797`78.21025950729067,s[8,5][t]->0.24090633228117474744656112566980464351618817958213614151882204028261460877623733421434729897017`78.22960944629526,s[8,6][t]->0.251490036493382785458846510045026368875483564943286876864350343699768199571436343880867172872953`78.24723110280743,s[8,7][t]->0.273769485604247957881466666203347883422288608489667846407477001937637232057219440990547007188944`77.7253633846222,s[8,8][t]->0,s[8,9][t]->0.06909524812949649757999431953794515900682378063581482068222354272787503695944387942669438761994`77.09301828677526,s[9,4][t]->0.234204493126917749695593110684689437008272030260295522468161718882586177496073148935497067827605`78.02259986803554,s[9,5][t]->0.241969306832140246659991287244717644437497344243378819376393134901921434384444729429533349892336`78.0100343883893,s[9,6][t]->0.247672632096309143554438793521313477237646866623043587583902937535197245063667660871395276150946`78.00222133282291,s[9,7][t]->0.255707787344911888401058806479304981720244155358146106717005312615956426907258864617293381032509`78.66066002903834,s[9,8][t]->0.243517948680056653723346086102258940910739805456367681428613042304298586182208291085550490336996`77.81812573513601,s[9,9][t]->0},
     precision = 80 },
     Off[NDSolve::precw];
     Off[SystemOptions::noset];
  g[x_,i_,t_]:= -p-(h x)/u[i]+(h sigma^2)/(2 u[i]^2)+t/u[i]+E^(-((2 u[i])/sigma^2)x) cee[i][t];
  G[x_,i_,t_]:= -(h /(2 u[i])) x^2+(-p +t/u[i]+(h sigma^2)/(2u[i]^2))x- (sigma^2) /(2 u[i]) E^(-((2 u[i])/sigma^2)x) cee[i][t];
  ss[i_,j_]:=(s[i,j][t]/.svals);
  
           (* The variables *)
           dvars = Join[Flatten[Table[With[{i=i}, {cee[i]'[t],F[i]'[t]}],{i, imin, imax}]],{err'[t]}];
           vars  = Join[Flatten[Table[With[{i=i}, {cee[i],F[i]}],{i, imin, imax}]],{err},
                        Flatten[Table[With[{i=i,j=j}, s[i,j]],{i, imin, imax}, {j, imin, imax}]]];
           (* The equations defining F[\[CenterDot]]'[t], cee[i]'[t] and err'[t] *)
           eqns = Join[
                       Flatten[
                         Table[                        
                          With[{i=i}, 
                               {(* The i \[Rule] beta[i] edge *)
                                If[beta[i]==i, \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(g[0, i, t]\)\)==If[\[Not]MemberQ[recurrent,i], -slack[i,i], 0], (* If beta[i] = i, g[0,i,t] = -U defines cee[i][t] add a possible slack for transient edges *)
                                   F[i]'[t]+\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(G[\(s[i, beta[i]]\)[t], i, t]\)\) - F[beta[i]]'[t] - \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(G[\(s[i, beta[i]]\)[t], beta[i], t]\)\)==If[\[Not]MemberQ[recurrent,i],slack[i,beta[i]], If[i\[DirectedEdge]beta[i] === badedge, err'[t],0]]],
                                (* The i \[Rule] tau[i] edge *)
                                If[tau[i]==i, \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(g[theta, i, t]\)\)==If[\[Not]MemberQ[recurrent,i],  slack[i,i],0], (* If tau[i] = i, g[theta,i,t] = M defines cee[i][t] add a possible slack for transient edges *)
                                   F[i]'[t]+\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(G[\(s[i, tau[i]]\)[t], i, t]\)\) - F[tau[i]]'[t] - \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(G[\(s[i, tau[i]]\)[t], tau[i], t]\)\)== If[\[Not]MemberQ[recurrent,i],slack[i,tau[i]], If[i\[DirectedEdge]tau[i] === badedge, err'[t],0]]]}],
                          {i, imin, imax}]],
                       {F[ifix]'[t]==0}]/.s[__]'[t]->0; (* By Leibnitz rule, the s[\[CenterDot]]'[t] values disappear *)
           (* Fix the initial values of the variables *)
           initconds = Join[Flatten[Table[With[{i=i}, {cee[i][gamma] == (cee[i][t]/.sol/.t->gamma),
                                                         F[i][gamma] == (F[i][t]/.sol/.t->gamma)}],
                                          {i, imin, imax}]],
                            {err[gamma] == eps},
                            Flatten[Table[With[{i=i,j=j}, s[i,j][gamma] == ss[i,j]],{i, imin, imax}, {j, imin, imax}]]];
           (* The equations defining s[i,j]'[t] *)                  
           seqns = Flatten[
                      Table[
                       With[{i=i,j=j}, 
                            If[i==j, s[i,j]'[t]==0, (* s[i,i][t] = 0 *)
                                                                      
                                     s[i,j]'[t]== (-\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],i,t]+\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],j,t])/(\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],i,t]-\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],j,t])+
                                                   If[0 <= ss[i,j] <= theta/.params,0,
                                                      -((-\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],i,t]+\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],j,t])/(\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],i,t]-\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[s[i,j][t],j,t]))toggless[i,j][t]]]], (* toggless[i,j][t] = 0 if 0 \[LessEqual] s[i,j][t] \[LessEqual] theta and 1 otherwise *)
                            {i, imin, imax}, {j, imin, imax}]]; 
           (* The discrete variables toggless[i,j] *)
           discretevars = Map[toggless@@#&,Cases[Tuples[Range[imin, imax], 2], {i_,j_}/;(\[Not](0 <= ss[i,j] <= theta/.params))]]; (* toggless for each i,j with ss[i,j] < 0 or ss[i,j] > theta *)
           (* Initial values for the discrete variables: The WhenEvent is triggered when the function values are equal. This should be based on the function values:
              If i > j, toggless[i,j] \[Equal] 1 if g[s[i,j],i,t] > g[s[i,j],j,t]
              If i < j, toggless[i,j] \[Equal] 1 if g[s[i,j],i,t] < g[s[i,j],j,t] *)
           initdiscrete = Flatten[Table[With[{i=i,j=j},
                                       If[0 <= ss[i,j] <= theta/.params, {}, 
                                          toggless[i,j][gamma] == If[((i>j) && (g[ss[i,j],i,t]>g[ss[i,j],j,t])/.sol/.rates/.params) || 
                                                                     ((i<j) && (g[ss[i,j],i,t]<g[ss[i,j],j,t])/.sol/.rates/.params), 1, 0]]],
                                       {i, imin, imax}, {j, imin, imax}]];                
           (* Events to watch for *)                                             
           whenevents =  Join[{WhenEvent[Evaluate[err[t]<=0],"StopIntegration"]}, (* Stop when the solution is feasible *)
                               (* Stop when the policy is no longer valid *)
                              Flatten[Table[With[{i=i, betai=beta[i]}, 
                                     If[betai==i, {}, (* Stop if s[i,beta[i]] falls below s[beta[i],beta[beta[i]]].  *)
                                               WhenEvent[Evaluate[\[Not](If[beta[betai]==betai,0, s[betai,beta[betai]][t]]<=s[i,betai][t])],{AppendTo[messages, {i,betai, beta[beta[i]]}],"StopIntegration"}]]],
                                     {i, imin, imax}]],                
                              Flatten[Table[With[{i=i, taui=tau[i]}, 
                                     If[taui==i, {}, (* Stop if s[i,tau[i]] is rises above  s[tau[i],tau[tau[i]]]  *)
                                               WhenEvent[Evaluate[\[Not](s[i,taui][t]<=If[tau[taui]==taui, theta/.params, s[taui,tau[taui]][t]])],{AppendTo[messages,{i,taui,tau[taui]}], "StopIntegration"}]]],
                                     {i, imin, imax}]],
                             (* Change toggless[i,j] to 0 when g[ss[i,j],i,t] = g[ss[i,j],j,t] *)
                               Flatten[Table[With[{i=i,j=j},
                                       If[0 <= ss[i,j] <= theta/.params, {}, 
                                          WhenEvent[Evaluate[g[s[i,j][t],i,t] == g[s[i,j][t],j,t]/.rates/.params], {toggless[i,j][t]->0}]]],
                                       {i, imin, imax}, {j, imin, imax}]],
                              (* When s[i,i+1] is too close to s[i+1,i], stop to recompute the slacks on transient modes *)          
                               Table[With[{i=i}, WhenEvent[Evaluate[s[i+1,i][t]-s[i,i+1][t] <= 10^-3], "StopIntegration", "LocationMethod"->"StepEnd"]],{i, imin, imax-1}]];                                     
                (* The slow step - solve the equations for the dvars to get the dbasis *)
                With[{dbasis = First[Solve[eqns, dvars]]}, 
                     (* Find slack values that work *)
                      With[{slackrules = If[Length[transient] > 0, NMinimize[Join[
                              (* Minimize the sum *)
                              {Plus@@Flatten[Table[With[{i=i}, {slack[i,beta[i]],slack[i,tau[i]]}],{i,transient}]]}, 
                              (* Subject to the conditions: 
                                 If s[i+1,i]-s[i,i+1] is "small", those two will not move closer together  *)
                              Flatten[Table[With[{i=i}, If[Chop[ss[i+1,i]-ss[i,i+1]- 10^-3] <= 0, s[i+1,i]'[t]-s[i,i+1]'[t]<=0/.(seqns/.Equal->Rule)/.dbasis/.svals/.sol/.rates/.params, {}]],{i, imin, imax-1}]],
                               (* and if  beta[i] = i or tau[i] = i, the corresponding slack = 0, otherwise, the slacks are non-negative *)
                              Flatten[Table[With[{i=i}, {slack[i,beta[i]]>= 0, slack[i,tau[i]] >= 0}],{i,transient}]]],
                              (* The variables are the slacks *)
                              Flatten[Table[With[{i=i}, {slack[i,beta[i]],slack[i,tau[i]]}],{i,transient}]]], 
                              {0,{slack[__]->0}}]}, 
                                  
                   step = 0;                         
                     (* Solve the differential equations *) 
                  With[{opts=SystemOptions[]},
                     SetSystemOptions["NDSolveOptions"->"DefaultSolveTimeConstraint"->10.`];                                     
                    
                          ndsol = First[NDSolve[Join[initconds, initdiscrete, dbasis/.Rule->Equal/.SetPrecision[Last[slackrules],\[Infinity]], seqns/.dbasis/.SetPrecision[Last[slackrules],\[Infinity]], whenevents]/.params/.rates, 
                                           Join[vars, discretevars],
                                           {t, -\[Infinity], gamma}, 
                                           DiscreteVariables->discretevars, AccuracyGoal->15, PrecisionGoal->15, 
(*MaxSteps->89,*)
                                           WorkingPrecision->precision, Method -> "StiffnessSwitching",StepMonitor:>(++step;dynrep = {Row[{"step =", step}],Row[{"t = ", t}],Row[{"err[t] = ", err[t]}]})]];
                              SetSystemOptions[opts];]]]]

Modified/Augmented for clarity and to provide answers: Implementing a more robust mechanism for addressing singularities yields a nice answer quickly. Streamlined and more fully explained code that solves and presents that solution is available at MoreDotsh@WolframCloud