Yes, building up the correct muscles will definitely be important, and doing circling exercises is one way to do that. But also make sure that she's bent correctly - if you let her circle to the left with a right bend, she won't be using the proper muscles. Do a lot of figure 8's where you pay very close attention to bending her correctly around each circle. Really make sure you have her moving off your inside leg to keep the correct bend throughout the entire circle.
As for circling until she's uncomfortable enough to change leads - I tried that with my horse and it doesn't work because he's so used to cantering on his left lead that he can (and will) canter small circles to the right on the wrong lead indefinitely.
PaintLover makes an important point: don't overdo it. As soon as you get the lead you're looking for, let her canter on it a little then praise her like crazy. You can build up slowly until she can canter full laps around the arena.
Another thing you might want to look into if you can afford it is having an equine masseuse/chiropractor look at her. If she has something out of line or her muscles are really tight, having some massage therapy or a realignment could do wonders.
(PS - Can you post a video? It'd be really helpful!)