Well, I see that you have to work with what you have , not what you might like to have.
Yes, you can canter a horse with leg on and on the bit. If the horse speeds up with leg on, then think of leg "down". If the horse does this it might be because you are "clamping" on. you would be better to think of thigh on, heel down. This way you have body weight and contact to the horse all the way down. When people clamp too hard with the calf, frequently the heel comes up and the rider will lose the stirrup. does this happen to you?
As for being on the bit at the canter, if the hrose IS on the bit, it helps the rider in many ways. If the horse is on the bit, he will usually flex at the poll, lift his back up more and be less on the forehand. All of these things make it easier for the rider to go with the horse and stay "in control". The horse should not stop just because you take up some rein contact.
It just seems that your instructor is having you do things that you are not ready for. She is not having you build a confident seat at the slower gaits, enough. It does help the rider to be able to make a connection via the bit to the horse, but if the rider cannot sit somewhat securely, then THAT is a whole that needs to be fixed first.
The horse will be able to read your lack of confidence and might be giving you a harder time than the others. If you had a secure seat you would be ok with laying a whip on him, right? You would know that most of the time spooks do not mean falling off (though falling off happens, no matter what. You know that, right?)
I just think that you might benefit from doing some lungeline lessons where all you did was build the muslce memory to be better able to sit up straight, and move WITH the horse.
But not to discourage you. You might be in a slump now, but dont worry. Slumps pass and then youll go up to the next level.
IF you wanted to post a video we might be able to see some points that are very easy to improve upon.?