How about on the lunge line? My horse has the same problem and doesn't like to pick up the right lead on the lunge. While riding he's fine, because I can get his hip in, etc. Even after a small jump (on a straight line), he'll choose the right lead on his own. So, he seems comfortable with the right lead, but just doesn't like it on the lunge!
Monte - 15 year old Paint/TB
Auric - 13 year old Arab