One of the horses I ride does the same exact thing. The only thing different is that he is missing a chunk of muscle from his left foreleg from an accident when he was very young. All his life he has had to compensate for that. His left lead canter is beautiful, the perfect western lope, while his right lead canter is gimpy and discombobulated. When I first started riding him, he wouldn't even pick up the right lead. That was in spring 2009. Now he is much more willing and his right lead is not so stiff and horrible. It will never be as nice as his left lead, but it has improved. The problem was mostly me because I did not know how to prepare him for the canter. He needed to be supple and going correctly. And then the rest of it was just getting him into shape.
I would canter him on his easier side first so that he knows what you're asking. It's also good for you to get a feel for what you want his right lead canter to feel like. After working on his hard side, I would end with another left lead canter so that you can end on a good note with him. Working on a large circle is a good idea because you will be able to have a constant bend. Think of doing a little shoulder-fore, even while on the circle. That will help his balance. Try changes within the gait. With the horse I ride, it helped when I asked him to lengthen his canter stride. Then when I came back to a more collected canter his was still pushing with his hind quarters. Once you are pretty solid on the circle you acn try to introduce some straight lines and different figures. Remember to have a good riding position throughout this! I know I tend to forget about my body and think only about the horse, but my body is what influences the horse. ;)