Getting a stronger bit is not the answer. There is a reason why he is being like that. You should do a lot of ground training with him to get him to respect you. There are a lot of natural horsemanship programs out there. By getting a stronger bit, you'll only be hiding the problem. And what happens if you do go to a bit a level up from a snaffle and that doesn't work? Are you going to go harsher? And what if that doesn't work?
I would get a vet out and check for any signs of pain. When was the last time his teeth were floated?