sorting - How to pass composite function list to SortBy?

In order to sort alphanumeric-as-string data of the form {"T3", "T14", "T1", "E2"}, so that "T14" comes after "T3", SortBy requires the tiebreaker function list:

{StringTake[#, 1] &, ToExpression@StringDrop[#, 1] &}

Which works as intended when this expression is inserted literally in SortBy. However, defining a utility function

mySort[x_String]:={StringTake[x, 1] , ToExpression@StringDrop[x, 1]}

doesn't work since the output is a list of expressions rather than a list of functions.

The alternative - to define a function via

mySort := {StringTake[#, 1] &, ToExpression@StringDrop[#, 1] &}

only works when the list to be sorted is 1-dimensional (as above) but not with lists of the form data2={"T3"->a, "T14"->b, "T1"->c, "E2"->d} where it is necessary to use SortBy[data2,mySort[#[[1]]]&].

Any alternatives that will work for general expressions?

Answer

I think this question admits an elegant solution. Here is my attempt: define a special wrapper:

ClearAll[sortFun];
sortFun /: SortBy[expr_, sortFun[funs_List, partFun_]] :=
   SortBy[expr, Map[Composition[#, partFun] &, funs]];

Now,

mySort := {StringTake[#, 1] &, ToExpression@StringDrop[#, 1] &}

and

SortBy[{"T3","T14","T1","E2"}, sortFun[mySort, Identity]]

(*   {E2,T1,T3,T14}  *)

while

SortBy[{"T3"->a,"T14"->b,"T1"->c,"E2"->d}, sortFun[mySort, First]]

(*  {E2->d,T1->c,T3->a,T14->b} *)

EDIT

Perhaps more elegantly

ClearAll[sortFun];
sortFun /: SortBy[expr_, sortFun[funs_List, partFun_]] :=
   SortBy[expr, Thread[Composition[funs, partFun]]];

and just for fun, another version:

ClearAll[sortFun];
sortFun /: call : SortBy[expr_, sortFun[funs_List, partFun_]] :=
   Block[{sortFun = Thread[Composition[##]] &}, call];