You should start with a good flat work, keep your horse focus on what you are asking him, change the routine as much as possible with every figure you can think about. Do a lot of transition, in particular walk-halt, trot-halt and also half halt every time you feel he is accelerating or running (usually this happens in the corners). Then you can start with ground pole and cavalletti work. First do them in trot, every time he runs, you stop him. If he do some strides before halting, you ask him to step back (you ask him the halt right after the pole and he does other 4 strides before halting, you step back for 4 strides). Don't consider it a punishment, you should do everything with calm. Also in&out exercises are very usefull because the horse has to mantain a smooth rhythm and he has to be focus.
I don't think that changing the bit is the answer: it's more mental than physical. If you can master the ground pole work and the little jumps, your horse will slow down, facing the jumps with calm and thinking about what he is doing.
I have a 6 year old horse, huge, green, strong and very disrespectful of poles and jumps. Working with this method, he is now very aware of what he has to do while jumping and how to do it. And i keep riding him in a loose ring snaffle.
Lots of small collecting jumps. Pole work is huge. Always asking your horse to come back to you when you land from the jump, sometimes you have to ask them to quietly halt, with good warning and not roughly, a few strides before the jump and after as well. But make sure not to be too aggressive when halting or this will teach your horse not to jump