Willig the freight train

We had a painful (emotionally and sweat-inducing) lesson today.
I have been losing my temper with Willig's antics. We started by me telling Shannon about how he won't quit swinging his head in the canter. (Sometimes I can see his teeth.) This led to us cantering around with my hands clamped on the breastplate (to see if it was my hands (giveaway: yes) or his head), but when we got to the scary end, he'd toss his head up and try to run. I'd react by see-sawing on his mouth, which would make him swing his head crazier. Shannon very calmly asked why I was ripping on his face (true answer: it makes me feel better) then pointed out it wasn't achieving any sort of goal - plus my goals were disorganized and inconsistent anyway, so how was he going to obey them?
Then we worked on the riding without hands, but I just got madder and madder because every time we'd head toward or away from the scary end (hint: in a rectangle, that makes everywhere but the short far end), he'd speed up. And sometimes skitter sideways. And I couldn't halt him. And so Shannon had us do a decent canter around, but he kept speeding up as we went past that end, so she had us keep cantering, until I completely melted down, tried to stop him, and couldn't, and jerked on his face all the way down the arena (this is longer than the long side in a full size dressage arena) trying to get him to stop before I just started crying.
So Shannon went and got a gag bit.
This helped a lot, although every time I'd apply any pressure, he'd toss his head up. While he still mostly blew me off - and this was the root of the problem - I had at least a tool at my disposal. Like the (now) trusty spurs.
And so this is it in a nutshell: bucking doesn't work anymore. spinning doesn't work anymore. his half ass rears don't work. But being a freight train does work.
Now I don't understand HOW freight train barreling around the arena is LESS work than just doing whatever I'm asking him to do (today: stop), but that's the next tool in Willig's toolkit, and like an idiot bipedal, I've chosen to wrestle with him - I mean, his freaking head probably weighs more than me - and I lose every time.
WHY does he do it? Because he's kind of a dick. Just like Shannon said the first time she rode him and John when I picked him up from training, and just like I'm learning from riding Mike's horses (and why my temper is getting so frayed and short with him).
We ended up with a fine series of fences, although they were baby fences, but since I started the lesson unable to halt, I guess that's progress.
We're going to try some stronger bits as another tool - not going backwards, but having something available to help correct his and my mistakes in training - and then I guess I'll see what he pulls out of his hat next.
We were both soaking wet with sweat by 1/3 of the way into the lesson. And I was crying and furious and frustrated with him, so I'm glad it was in front of Shannon during a lesson.
She said I have got to keep my cool. Pretend like I'm in a new arena and have no expectations about that end. Don't circle him anymore, but make him stay on the rail. If he's bad, he has to back or leg yield or shoulder-in. Try the harder bits and don't get in a wrestling match with his face. And be clear in what I want. If I want him to halt, make him halt.
Interestingly, this seems to be an extension of my Mike lesson, where Mike pointed out he was pretty much ignoring me. I think that's what's happened as this week has gone on - what makes me livid is when he just totally brushes off my aids and does whatever he feels like. I haven't known what to do when he does that.