Dr.Cook bridle! I had the same problem and now my horse is ama
I suggest training with speed transitions and ground pole work. If you are really want to try a new bit I suggest a three piece Wilkie but.
You don’t have to nessasarly change the bit, have you tried putting ground poles as a bounce before and after the jump, that’s what I did for my horse and now she is really good about not rushing/running through the jump. I also would sometimes make her stop in a straight line if she was getting to strong.
He just runs in jumping, it doesn't work. I've tried a kimblewick and all types of snaffles. Loose and eggbutt rings, d rings, Pelham baby Pelham. I have tried bitless but he just doesn't understand. Could it be a thing he learns ? He understands the turns but I don't get any support or control.