Back to OPs bit search, QHs often have smallish muzzles and shallow mouths. It could be the mouthpieces you have tried are too fat for her and some might have too many moving parts. My experience with horses fussy about bits is experimenting with thinner mouthpieces with no more then a single joint hung a hole lower then standard can solve a lot if problems…or hung a hole higher then standard. Often get into trouble with too wide a mouthpiece too, some don’t care, some spend the whole ride trying to spit it out. I used a 4 3/4 on one QH, which is Pony sized in other disciplines. Measure her mouth where the bit sits-use a piece of string then measure that.
Bits we think they will like often aggravate them, which aggravates us. That big fat mouthpiece we think looks soft is actually uncomfortable for them, My fav bit is a small custom, loose ring with thin mouth and small rings, copper laced blued steel mouth intended for schooling Reiners. I used it at home on my stout TB show Hunter with dainty muzzle and shallow mouth. A hole loose, horse picked it up and carried it well, never got fussy in it even though it did in just about anything else. Showed in a mullen mouth dee ring with no moving parts.
There is an old technique of tying a light snaffle onto the halter and letting the horse live it it to get them to accept its presence in their mouth. They learn to eat, drink and sleep in it. It works quite well. Obviously…there are some safety considerations, I used easily breakable thin cotton shoe laces and colt was confined to stall or small corral/pen with nothing to snag on and out of reach of nosey neighbors
Sometimes the root problem is accepting the bit itself in their mouths., not the signals and pressure it delivers. Worth a shot.
The issue with staying in a hackamore is its not acceptable on a mature horse in many competition arenas. There’s nothing wrong with staying in a bosal if OP doesn’t want to compete in those after the horse “ages out”
