I found that harder bits usually don't help with hard mouthed horses. We tried it with our akhal tekes and their mouth became more and more harder, at the end it looked like they had no bit in their mouth. Nor with the 3 ring and of course with martingal. No effect. They still run away - under the bit.
But our trainer said that if your horse don't understand what you want by the bit, you have to try another way to tell her what you want. So you may try this method:
When the horse starts a fast galopp instead of a slow canter, try to stop by the bit for once. If she does not get back to the asked gait, suddenly fall into their back with your bottom. Yes, it is a little bit painful for her, but you get two advantages by this:
1. You make her paying attention to you. Falling into her back means. "Hey, I've told you something recently and you did not pay attention!"
2. You get her out from the rythm of the fast gallopp, this will be uncomfortable for her. She will surprised and if the bit is on her teeth, she will drop it. If you fall into her back more times she will try to move in a less uncomfortable way, probably she will get back to canter or to trot.
But beware of bucking, they sometimes buck because of the sudden impulse coming from the rider on their backside, don't take care, follow it until she slows back. But still hold the reins and sometimes give her slowing orders with it.
She will learn after a few times that if she wants to avoid this uncomfotable feeling, she has to take care of the informations coming from the bit.