Here is my experience. Take it FWIW:
For sitting the trot, I had to overcome my tendency to brace against the stirrups. I ended up lengthening them a hole at a time until my feet barely touched them. That worked fine for trotting, and helped keep me on when my horse would twist or spin (spooky mare).
But the motion of a horse's back in the canter has a lot more power, and it simply threw my far enough out of the saddle that my feet would lose contact. That was in part because I couldn't get myself in synch with the horse's back, but I think it is also due to the amount of power going thru the horse's back at a canter.
I ended up doing a couple of things. First, I had to accept the idea of riding the canter more forward, in a half-seat (or my *******ized version of one). I simply couldn't learn the horse's motion without cantering, but I couldn't canter until I learned the horse's motion. Cantering in a half-seat allows me to A) get off to a good start so the horse is happy about cantering, and B) lets me settle back at my own pace, as we are cantering. That way I'm only doing it once I can feel the horse's canter, rather than guessing at it.
Second, I did need to shorten my stirrups, but only by about 1-1.5 inches. So if the stirrups are more than a couple inches shorter than you are used to, it isn't needed for cantering. If I shorten the stirrups much more than that, I still start to brace against them and then I bounce at ANY pace. From what you wrote, I'd ask for longer stirrups...
Here are my two favorite links on cantering. Much of it applies to sitting the trot as well: