The pony I leased a few months ago had the same issue, but instead of his old owner she smacked on a kimberwick and he was better... Still rushed, but certainly not as much.
When I started with him, I immediately started doing ground poles (just trotting) till I could get him to stop in the middle, before, and after the poles. Then I picked up a canter and repeated that same step. When we jumped, I put up a very small (about 6 inch crossrail) and we trotted over it. At first I halted before it, and once he stopped prancing we went over it, and we also halted after.
After a few months of doing that, he was doing MUCH better. My tips for you is to do the exercises above, and DON'T go bigger or faster till he's doing a western pleasure jog over them. And please don't put on a harsher bit, all that will do is BLOCK the speed, not contain and put it elsewhere. Good luck!