Drop Cap on right aligned paragraph/title

James's and Barb's suggestions combined produced below script. It simply implements Barb's suggestion to add left indent until it looks good. It could be refined, see how you go.

To use it, first set right-indent in the paragraph style. Then place the cursor in one of the paragraphs that need to be fixed and run the script.

(function () {
  app.scriptPreferences.measurementUnit = MeasurementUnits.POINTS;
  var pstyle = app.selection[0].appliedParagraphStyle;
  var plength;
  var pp = app.selection[0].parentStory.
		paragraphs.everyItem().getElements();
  for (var i = pp.length-1; i >= 0; i--) {
    if (pp[i].appliedParagraphStyle == pstyle) {
      plength = pp[i].lines.length;
      while (pp[i].lines.length === plength) {
        pp[i].leftIndent += 2;
      }
      pp[i].leftIndent -= 2;
    }
  }
}());

Ok, great. Glad you have a working solution. 

~Barb

I am not sure drop caps can be used with anything but left alignment. You could simulate it with an anchored text box for the cap, but all application and positioning would have to be manual.

A script or two might be devised to automate some of the work.