I agree with what Buck said. A horse needs to know how to respect a snaffle before it is moved up unto a hackamore.
Personally, I would want the horse in a snaffle. Like has already been stated, your horse should be able to flex easily and willingly. Once you can get her to do this, I also get them to learn to disengage their hindquarters. The softer and more supple your horse, the faster the run.
If I read right, you said she doesn't really like to respond to woah when doing slow work. I would fix this. This may be just me, but I want things to be perfect at the slower gaits before working on the quicker gaits just because I feel it gives them a better foundation. I ride every pattern the same at a walk or a gallop.
Some people I know don't like her, but Charmayne James has a great book out that breaks down barrels and has really helped shave time off.
As far as head tossing, I would want to fix this too. (If it is just her being antsy and not a pain issue). Too many barrel horses get away with ignoring their rider because they are excited. Mine used to do this, and the way I fixed it with him was everytime he would start getting figity I would either circle him, flex him side to side, or make him back. This is a lot more work for him than just loping along, so it worked. It may be worth a try.
I don't remember if I read it or not but what kind of hack are you using on the horse?