This may not be a popular answer, but I would suggest adding a little bit of candy, sugar or something your horse loves in your hand that feeds to the bit into his mouth. That will get him to open and begin to look forward to taking the bit.
I wouldn't up the severity of the bit. Perhaps the snaffle is painful or uncomfortable. Have you tried a french link? Maybe a totally different type of bit will provide him more comfort.
I recently had a mare in training that was very resistant. After ticking off all the items on my checklist such as saddle fit, teeth, back pain, etc I finally resolved the issue by putting her in a Myler combination bit. It works off nose and chin pressure long before the bit is actually engaged. She is so much happier. She isn't perfect but for sure the tongue pressure on the snaffle gave her anxiety and a will to fight. Good luck!