I agree with Saddlebag, his problem may just be a low pallet, and the other bits just don't fit into his mouth right. I would definitely use something with either the french link, or the bean link in the middle as opposed to a plain snaffle, because of the nutcracker action. Herm Sprenger makes a bit specifically for low pallets, found it in the dover catalogue.
I rode an Appy with a low pallet, and had a hard time finding a bit that he didn't act like he was gagging on. Constant mouth gaping, a bit of head tossing, tucking his head to get away from the bit ect. After the first couple of rides where it was obvious it wasn't him testing a new rider, or having a bad day, I put the bit in (regular plain single jointed snaffle) and pulled up his lip, and watched what happened when I put pressure on the reins, and sure enough there was no space even when he opened his mouth, and whenever I put pressure on the reins, the joint jabbed him in the roof of the mouth no matter how soft I was. For him personally we switched to a jointed port bit, and afterwards he was great. No more head tossing, no more gaping mouth ect. But he was a western horse, hence the ported bit.
Good luck, if it helps, you should get onto the USDF website, and look up the rules and regulations for bits, and see what bits are legal at what levels. I think you can find jumping regulations at USEF though I'm not positive.