I'm assuming your application is offline-enabled. Are you using RDL for something that grids don't support?

If you're on Pega platform 7.3 or beyond, you can stay with grid because grids (Responsive, Mobile mode) supports majority of functionality that RDL provides. I'd advise you go with sorting JS for RDL only if you hit major roadblocks with grids.

You can use same custom populator to sort data page. Once you have the filtered records, add the sorting code too. 

function D_UserWorkListFiltered(dpPage, params){
  	  var cc=pega.u.ClientCache;
      var sortParam = params.sort;
      var sortedPL = dpPage.put( "pxResults",[] );
      var masterUserWork = cc.find("D_pyUserWorkList.pxResults").iterator();
      while(masterUserWork.hasNext()){
        var workPg = masterUserWork.next();
        // Filter condition here 
          sortedPL.add().adoptJSON(workPg.getJSON());
      }
  		//Sorting on task label
      if(sortParam === "LABEL"){
        var res = sortedPL.pxResults;

        res.sort(function(a, b) {
          var labelA = a.pxTaskLabel.toUpperCase(); // ignore upper and lowercase
          var labelB = b.pxTaskLabel.toUpperCase(); // ignore upper and lowercase
          if (labelA < labelB) {
            return -1;
          }
          if (labelA > labelB) {
            return 1;
          }

          // names must be equal
          return 0;
        });

      }
}

Can you give more information on what doesn't work? The alerts that you put, are they coming as expected. 

Looking at the code, if SearchUrgency param value is say 40, you're adding all work with urgency 40 to the list. Then you're sorting by comparing same pxUrgencyAssign property value which will be 40 for every record, sorting will not take place in that case.