At what point do I move up?

He doesn't canter on a lunge (thats a whole other topic in itself), but I know that he'd be more than happy to move into a canter with me on his back. He has a very nice balanced trot with no one on him, but he still throws his head with me on him, probably because I don't like his leggy trot that he does when he is trotting on the lunge.

The few times that we have gotten him into a canter on a line, he charges forward with his head and looks very racehorse-ish, which is what I don't want him to do and then completely ignore my cues.

As long as you keep it very simple for him and optimize his chances of staying balanced, I don't see any reason why you cannot give it a try. I would get him into a nice forward trot on a large circle. Make sure he's balanced and bent slightly to the inside to increase the chances of him picking up the correct lead. Left lead is almost always preferred by ex-racers. Make the cue very simple, sit tall, bring your inside rein forward a hair to free up his inside shoulder, and slide your outside leg back during the up beat of the trot. Make sure to not pull on his mouth if he canters. He needs to know he did the correct thing. If he does canter, only keep going as long as he keeps his balance. If he starts to lose it, go back to trot or walk, and then regroup and ask again. If every time you ask, he just rushes into a hurried trot, he's not balanced enough to canter and you'll need to make some adjustments.

His balance isn't so much of an issue to me as maintaining control is. The more often we trot during a session, the less he tosses his head, and I've been consecutively going out to ride him for three days now (usually I'll do one day on and then one day off) and he seems to be doing better.

Although he's never done this before while trotting, if he doesn't want to turn left (which he usually doesnt), he'll stick his nose up in the air and turn his jaw/jowls out and start walking sideways--basically avoiding the pressure from my hackamore. I am mainly worried about him doing something similar when we first start cantering, and was more along the lines of wondering what indications to look for that would say he's got his head on square enough to canter without getting a "race horse brain" and just doing as he pleases.

Ahhh. Yeah, I guess I'd be concerned in that case. Any reason in particular you're using a hackamore? I'm all for the less the better, but if he's not listening to you to the point where you can't even get his attention at the trot, maybe a bit might be in order for awhile until he's better trained to your legs and seat?

If you're set on the hackamore, I'd start leg yielding the crap out of him to get him listening your aids. Every time he blows you off turning left, leg yield him into that right rein until he thinks you've lost your mind and agrees to listen to you. I'm honestly not sure how it works with no bit, but that's all I've got for a suggestion.

It may sound like I'm accomodating him too much (I probably am, lol) but he can not STAND to have a bit in his mouth. When I first got him, I used a bit on him for three weeks, and every time I went to put the bridle on he'd toss his head and wouldn't open his mouth no matter how many fingers I had in there. His teeth had just been done at the time, so I knew that wasn't it, and then when I would finally wrestle it on, he'd try to push it out of his mouth and hold his mouth open like it was painful. I have experience in using a hackamore, so I just went out and bought one and on the first day we were out in the ring and he was responding perfectly.

For an OTTB, he actually listens quite well (I can keep light pressure on his nose and he collects, and if I let go he extends out, stuff like that) and he has no problem transitioning downward when I cue him, I am just assuming once he gets moving into the faster gates, he'll get more obstinate.

If you're confident in using your brakes, maybe just let him canter a few strides and downshifting back to trot before he has time to take over and act like a goof. Use the transitions to optimize your success. He sounds responsive. Maybe he'll surprise you and fall into a nice rythmic canter. Only one way to find out!