I had a horse like that. If I had her now, I wouldn't worry so much-- I'd just let her go, until she found her balance. You need good footing, and a big area. Give lots of praise for stopping, and when the gallop feels fairly balanced, I'd try spiraling into the circle a bit. Sit up and very still.
With my horse I couldn't figure out why she kept running, when her trot work was going so well. One day it was slick footing, and her legs slid right out from under her, and down we went. And it was THAT which initially slowed her down. She went so carefully after that, though of course I didn't canter much more in that mud. (But I don't recommend tripping up your horse, although I know there are trainers who can do it!)
Not long after, I think it was, we got a very mellow horse with a long, rhythmic canter, and one day my rusher watched her whole lesson. And the next time we cantered, she was slow! I thought it was a fluke, but she really did learn by watching. You can try that too.