The biggest bit change I would make would be to experiment with different snaffle styles and materials, to find something that makes him happier. Smrobs said it all. Make him responsible for going at the speed you want in a snaffle, then, if you want refinement and the option to give a more precise (not stronger! While I don't plan on ever putting one in my boy's mouth, even the spade bit was originally designed for excellent hands to give the most subtle of signals!) The vast array of bit options are available for degrees of precision in cues and comfort needs for the horse, although there is a slew of "quick fix" gimmicks to be careful of, not as an excuse to upgrade in "toughness" when your horse gets duller and duller.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown