I would try schooling before changing tack. Jumping on a circle is a great exercise for a horse who likes to run. They have to establish a rhythm in order to keep their balance. Keep the fence small and the circle about 20-30m. I would also jump him a couple of times over a small fence with poles before and after a few times a week. The ideal time is half way through a flatwork session when he is listening to you and he then has to learn to relax and settle back to flatwork again. After a week or two he is less likely to get so excited by it.
As counter-productive as it sounds, put on more leg! A lot of times with horses that get too excited they end up unbalanced and running on the forehand. The only way to correct this is by encouraging their hind-quarters underneath their bodies. This will also stop your horse from putting in an extra short stride in front of the jump, and also help your horse throw a better jump in general as he's able to use himself more effectively. To teach your horse to accept your leg pressure riding a leg-yield on a circle is a really good exercise, as it will also get him lighter on the fore-hand. Also, try to keep your leg on during downwards transitions, to keep him "together" and teach him that when you close your leg it means he must collect himself up instead of simply running forwards. Then for jumping, with my horse it helped to build loads of spooky jumps, that he backs off a bit more and to allow you to put your leg on him to jump. Also just going over two poles on the grounds/small jumps set 5 strides apart, and then adjusting his stride from 5 to 4 to 6 etc. Normally this makes them really nice and responsive, as well as them starting to "bounce" more instead of just galloping flat-out over the poles
Equipment wise: I also don't know what bit and noseband your horse has so it's hard to say. You could change your bit onto slightly stronger one but don't go from a snaffle to a Pelham straight away. Play around and check what are the stronger bits than the one your horse currently has and then have a look at the noseband. Try grakle or drop noseband and see what your horse response is like. If it's willing to work like that or maybe shows a bit of discomfort. :))
I would also try some grid work before actual jumping to get the horse's mind focused and so all the freshness comes out of him during this exercise.
And maybe put some poles before the jump to get the horse thinking forward and thinking about strides being more even and going in the same rhythm
I agree with Emilee and you can also use your voice to calm down your horse and use your body. In most cases it is because the rider gets nervous/excited/forgets how to ride and just rushes/tenses up. If the rider stays calm, relaxed and effective the horse will normally be calm and relaxed.