My horse is sensitive mouthed as well. I recently began riding him in a Korsteel Regular D-Ring snaffle bit and it works wonderfully. My gelding is quite wild at times, but I find the bit is soft enough for his sensitive mouth but keeps him controlled. I hope this helps!
I've found that my mare was flinging her head a lot and resisting pressure in a snaffle as she didn't like the nutcracker affect so I switched her into a happy mouth loose ring Mullen mouth and she works really well with in it.
If it's not working then you must look into the reasons as to why he does not respond to the bit you are currently using rather than finding a stronger bit. If he won't respond to the one he is currently in, what makes you believe he will be any better in a stronger bit? You cannot find a solution if you do not know the cause.
Check to see if your horse is in discomfort with the bit. Many popular signs of discomfort in the mouth are:
- head tossing
- high head
- reluctance to slow down
Horses are flight animals so naturally, if they feel pain or some form of discomfort, especially in the mouth, they will attempt to run away from it. If you give your horse a cue to slow and he speeds up, this is either due to the bit causing him pain or he simply does not understand the cue to slow.
I recommend that you start on the ground first, asking him to flex one way and another to make him soft to the reins. You should be able to pick up one rein and your horse should give to that pressure if you have been consistent and clear. Using pressure and release really helps them to understand how to be soft to the reins. Not only does flexing your horse relieve tension, but it also shows them that it's easier to be soft on the reins rather than fighting the contact. If you need any clarification of pressure and release please don't hesitate to message me.
It's the training and effort put in that ensures that your horse responds better to you; not the metal you put in their mouth.
Snaffles work by putting pressure on the bars and the roof of the mouth. To reduce the pressure on the bars and increase pressure on the tongue, try a lozenge bit. If you want pressure to be distributed more evenly across the mouth, a mullen may work best. If you find no other bits work, try bitless and re-train in a hackamore or bitless alternative.