Dial it back - a lot.
Try walking over fences for a couple weeks (about 18 inches and under). When he does that calmly, trot fences for...until he stops rushing...could be a week, could be 6 months. If he gets strong trotting go back to walking until he is calm. You can trot over jumps as high as he can handle.
This is what I am doing with my insanely athletic ex-foxhunter, who can jump the top of the standards with ease, but feels the need to hurl herself at itty-bitty baby jumps. I 've trotted her up to 3 ft so far and we are "almost" ready to canter jumps again. Taking it back a notch - along with A LOT of flat work - has made more difference than any amount of rollback turns ever could - although we do a lot of those too!
Also, if you are anxious and your horse is sensitive, he will feel you. This will go against everything you were taught, but try getting slumpy and relaxed before a jump so that by the time you take off you are already there - this is good to practice on those walk and low trot fences since you're unlikely to encounter the rapid, dirty stop. When you are doing flatwork, try getting all relaxed like this too - almost in a slumpy jump position, but not quite. This will help your horse learn to stop associating your forward movement as "time to jump - woohoo!"
On the bit question, I use a gag - the Mikmar Watson 3 ring. My bit, used properly, can be softer than a snaffle, but when I need to break my horse up, which happens sometimes, it is there. Although some horses simply won't tolerate a gag, if your horse is throwing its head a lot in the gag, you are probably being too harsh with your hands and not giving enough when your horse gives. You can't just hold on these bits (not that you should on any bit) - you have to give and take and supple and be really light, only engaging when you have to. The bit doesn't replace the work, it simply supplements it for when you need that extra leverage and to reinforce your leg and seat aids. Also, these bits can also be bad to use on a nervous jumper if your timing with your hands releasing over jumps isn't perfect. Just a couple snaps over the fences and you'll have a whole new set of problems on your hands. Just something to consider if you are going to keep working with the gag.