I would recommend lots and lots of transitions, also some general conditioning work might be good, this kind of behavior is usually a sign that the horse is not balanced and strong enough to carry himself in the canter. He uses the bit as a "fith" leg, which helps on a straight line. Cantering through corners requires even more strength from the horse, so that's why he falls back to trot.
Do lots of counter canter. Maybe half the circle counter bending and then normal flexion for the 2nd half. With him tucking his head in it doesn't look pretty but widen your hands and lift them up every time he does it till he learns where you want his head. He might just be unbalanced. Everything takes time 😊 Good luck 😊