Apply UpValues before Listability

Question

I'm trying to modify Plus but am running into trouble with it being Listable:

ClearAll[f, g, h]
Attributes[f] = {Listable};
h /: f[x_h, l_List] := 0
h /: g[x_h, l_List] := 0
f[h[1], {1, 1}]   (* {f[h[1], 1], f[h[1], 1]}, not OK I want 0 *)
g[h[1], {1,1}]    (* 0 as expected *)

How can I make the UpValue (or equivalent) have higher priority than the listability?

EDIT: I ended up wanting to do this again and figured I'd fix the Plus properly. Here it is working using Sashas answer and Mr.Wizards $Pre method:

    $Pre =.
ClearAll[myPlus]; Attributes[myPlus] = {Orderless};
Unprotect[InterpolatingFunction]; UpValues[InterpolatingFunction] = {};
InterpolatingFunction /: 
 myPlus[y_InterpolatingFunction[t_Symbol], l_List] := 
 Interpolation[
   MapThread[List, {y["Grid"], l + # & /@ y["ValuesOnGrid"]}], 
   InterpolationOrder -> First[y["InterpolationOrder"]]][t]
myPlus[other__] := +other
$Pre = Function[x, Unevaluated@x /. Plus -> myPlus, HoldAllComplete];
    Protect[InterpolatingFunction];

    y = Interpolation[Table[{i, RandomReal[{0, 1}, 2]}, {i, 1, 10}]];
    ParametricPlot[{y[t], y[t] - {1, 1}}, {t, 1, 10}]

Answer 1

This seems disgusting, but here it goes

h /: Plus[x_h, l_List] :=
 withPlusListability[True][

  blabla; 0
  ]

withPlusListability[bool_: True | False] := Function[code,
   Internal`InheritedBlock[{Plus},
    Unprotect[Plus];
    If[bool, SetAttributes, ClearAttributes][Plus, Listable];
    code
    ], HoldFirst];

withH = withPlusListability[False];

So

withH[
  Print[h[3] + {4, 5}];
  Print[h[3] + 7];
 ];

prints

(*
0
7+h[3]
*)

While you evaluate code iniside withPlusListability[True|False], it takes care that Plus has|doesn't have the Listable attribute, without changing it globally. h's definition will only have a chance of matching with an unlistable Plus.

Plus is one of those symbols that are so special you really try not to mess with. As @Mr.Wizard warned, this will likely break for packed arrays, because it probably has been optimized to cut some corners.

Answer 2

Contrary to Rolf Mertig's comment I believe $Pre does work.

First define your function:

h /: myPlus[_h, _List] := 0
myPlus[other__] := +other

Then set $Pre:

$Pre = Function[x, Unevaluated@x /. Plus -> myPlus, HoldAllComplete];

Test:

h[1] + {4, 5, 6}

0

z[1] + {4, 5, 6}

{4 + z[1], 5 + z[1], 6 + z[1]}