The bit holder that Jackie Cochran mentions could work, but would not be show-legal. That may not matter to you.
Another possibility would be to put a softer (literally softer) bit in the mouth, like an HS Duo bit or a Nathe bit, maybe a mullen mouth. Both of these bits are soft plastic, very pliable and unlike the hard plastic Happy Mouths.
I’m thinking that the soft plastic may not cause pain to the back molars in the same way that a metal bit might. You could also try a leather bit. They’re a little harder to find.
If the horse is doing well bitless, and you don’t care about doing rated shows, then you might just want to stick with what works.
Good luck!