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I know how to add Callouts to the outside of a PieChart, but I would like to add inner ticks like this:

enter image description here

Note the 3, 6, 9, 12 ticks in the above image. Are there any simple options that I'm missing? Can ticks and inner callouts both be set?

Here's a MWE:

PieChart[{3, 4, 2, 3, 2}, SectorOrigin -> {Automatic, 2},
 PlotRangePadding -> -10, ImagePadding -> -20, Frame -> False, 
 ImageMargins -> -10,
 ChartLabels -> Placed[{"1", "2", "3", "4", "5"}, "RadialCallout"]]

enter image description here

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ticks = Join[Thread[{Range[π/2, 2 π, π/2], Reverse@Range[3, 12, 3], 
     {0, .05}}, List, 2], 
   Thread[{Complement[Range[π/6, 2 π- π/6, π/6], Range[π/2, 2 π, π/2]], "",
     {0, .02}}, List, 1]];
pc2 = First @ PieChart[{1, 1}, SectorOrigin -> {{0, 1}, 2}, 
   ChartStyle -> Directive[EdgeForm[], FaceForm[None]], 
   SectorSpacing -> {0, 0}, PerformanceGoal -> "Speed", 
   PolarAxes -> True, PolarTicks -> {ticks, None}, 
   PolarAxesOrigin -> {0, 1/10000}];
axis = pc2 /. t_Text :> (t /. Scaled[{0., 0.}, a_] :> Scaled[-.05 a, a]);

opts = Sequence[SectorOrigin -> {Automatic, 2}, PlotRangePadding -> -10, 
   ImagePadding -> -20, Frame -> False, ImageMargins -> -10, 
   BaseStyle -> {FontSize -> Scaled[.04]}];
PieChart[{3, 4, 2, 3, 2}, opts, 
 ChartLabels -> Placed[{"1", "2", "3", "4", "5"}, "RadialCallout"], 
 Epilog -> axis]

enter image description here

A more convenient approach is to use ClockGauge to create an angular axis:

ClearAll[angularAxis]
angularAxis[o:OptionsPattern[]][so_, t_: Range[3, 12, 3], tl_: {20, 12}, sd_: {12, 5}] :=
  {First[ClockGauge[{}, ScaleOrigin -> so, ScaleDivisions -> sd, o, "TickLengths" -> tl, 
      GaugeMarkers -> None, GaugeFrameStyle -> Directive[EdgeForm[], White], 
      TicksStyle -> {Thick, Thin}, LabelStyle -> FontSize -> Scaled[.03]] /. 
    Text[a_, b___] :> Text[a /. Except[Alternatives @@ t] :> "", b]], 
   Circle[{0, 0}, so]};

PieChart[{3, 4, 2, 3, 2}, opts, 
 ChartLabels -> Placed[{"1", "2", "3", "4", "5"}, "RadialCallout"], 
 ImageSize -> Large, Epilog -> angularAxis[][2]]

enter image description here

Use

angularAxis["LabelSide"->Right, "TickSide"->Left, TicksStyle->Directive[Thin, Black]][2]

to get

enter image description here

and

Epilog -> angularAxis["LabelSide" -> Right, "TickSide" -> Left][1.5]

to get

enter image description here

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