I will probably get shot for saying this, but I disagree that snaffles are always the way to go. They can be just as harsh when your hauling on your horse's mouth to get them to listen. I had a very sensitive, responsive arabx and I rode him in a snaffle for years. He would pull and run through that bit as much as he could. I switched barns and coaches, and my coach suggested a kimberwick. Changed everything. He had respect for my aides, I was not in his mouth at all, which to me is the most important thing. And, he was happier.
My farrier said once, if you taught kids to ride in a shank bit on a good old horse, they would never learn to pull on a horse's mouth. I agree with this. I rode lesson horses as a kid with hard mouths in a snaffle, and thats what I learned, was how to pull on a horse's mouth.
As for the bitless bridle, I've tried them, and they are not my preference.
I think you should try different bits before crossing them off your list.