A horse that has energy and drive towards a jump is a GOOD THING! Unless you are doing hunters it’s ok for him to get forward to a jump…you just need to be able to control it.
Put your heels down and get your legs under you, and going into the jump SIT DOWN IN YOUR TACK. This will make it so he cannot pull you forward out of your seat, take his head and run. He needs to keep the energy, but sit up, lift his head and tuck his hind end under himself to get an uphill, light canter.
Also, despite what many people will try to tell you, not every horse is going to be a good, controlled jumper in a gentle snaffle. In fact, most will not be. Try something like an elevator or gag that you can ride with double reins to have a snaffle rein and a rein with more power. Elevators are great for horses that want to lean on you because they naturally encourage horses to lift their forhand and stop pulling downward.