My avatar is Tara, but that's just a grooming halter she's got on.
I do work with her daily, but don't ride often due to snow and ice that's been a constant companion for awhile now. She's very herd-bound (well, horse-bound) and when I've ridden her with her best friend, she's much better. Still chomps, but doesn't tuck her head in and avoid the bit quite as much. So perhaps it's just an attitude thing...if I lead her away from him, she tries everything to get back to her friend, bucks and rears and backing up included. I know that we need a lot more work on that, and hopefully an improvement in that area will help this issue as well.
I will also try a hackamore! I'd love to use one if it is effective, and if it is, at least I can do two out of three phases in one