My horse had a similar issue when I first bought him– it was like an all or nothing canter. He had very little muscle though– once he was in a regular program with me (Riding him six days a week) he started to gain muscle and I eventually put him in bungees, which helped him balance and build his top line up. his canter has gotten much more balanced, and as a result, much slower. I would also suggest counter-cantering to really teach the horse to balance themselves (will also help with lead changes). Another thing was putting him on a Vitamin E supplement– I use Elevate. It’s really great for a whole variety of reasons, and if there is any soreness that he is experiencing, it will only help!
I dont know how old your horse is (mine was 4 when I got him) or whether or not he is underdeveloped, but hopefully some of this info will help.