what is it she does to let you know she is unhappy with the bit? It may not be so much she is unhappy with the bit but has found a way to work around it. I have used a hackamore before, I'm not against them if used correctly but I believe a bit is the best option.
If your horse takes the bit willingly but then develops problems it could be anything from your hands to attitude or lack of training and willingness to accept the bit.
IMO, if you are concerned about not having control I would work on the bit issue and forget the hack. Control to me is having a good working relationship with the horse whether it is in a bridle,halter or hack so switching really doesn't solve the underlying issues with resistance.
I completely understand your concerns, I have a horse who was ridden by a heavy handed child for years and he is resistant to bit contact on his mouth and his teeth are fine as well. We chose a bit we knew was a good gentle bit if used correctly and we have stuck with it. There is still some resistance when engaged but it is getting better and since he is neck reined and works off the seat and leg we rarely pick up the reins with him anyways
Good luck, if you decide to use a hack, just remember to introduce it like you would any other tool and do so in a safe confined environment in case she does not respond to it. A hack requires a horse to willingly give his head and not nose out on you because if they resist or pig root with one on it is quite easy for them to get away from it and take away any control you may have had