Clear packing tape will work. I use clear monocote, but that is me. Sealing the gap is the easiest thing to do for a start. I would try it first and see how much it improves. Only takes a few minutes. Be sure to clean the area well with alcohal before sealing. I would say that the % of improved effectiveness would depend on the size of the gap your sealing.
Be sure also to move the control to maximum before you apply the sealing material so as not to create any binding and allow full travel.