I have lessons with an instructor: it was her that suggested the stronger bit, too. We've been doing circles, trotting work and whatnot, and they help sometimes, but only while we're doing them or right after we did them.
Despite the resounding negative response to the idea, I have put a new bit on her and, short-term or no, it's working. She knows exactly what it can do, and is far more responsive when we use it, allowing me to ride with a looser rein and way lighter contact. Rather than dealing with the rushing and the pulling until she tires herself out, the last few times I've ridden we've had about ten minutes of head-tossing before she settles down.
Because of that, we can work on smaller circles and balancing work (Sempre's right in that a lot of it's a balance problem), bringing it back to basics as was suggested and having a way more efficient time of it. Walk/trot without fuss is a relief, you know? Being able to bring her down to a walk and have her actually stay there, rather than dancing and mini-trots. With any luck, bending work from there'll help with the leads, and that should be coming on well given a bit longer.
And it prevents the whole anger thing from getting in the way (right again), 'cause there's so much less to get angry at.
So, stuff's getting better, basically. Or at least it has excellent potential to do so.
Yay. Thank you.