Thanks for the advice. I'm working with a trainer right now, but she recently left the barn and I don't get lessons nearly as often (which is why I'm here). I'm taking the knife edge off asap, too.
The problem is, when I loosen the reins, he goes faster, especially at the trot. He likes to rush and you really have to haul back to get him to slow down.
Rushing is a balance issue and no amount of bit (or bit changes) is going to fix that. If the horse rushes even on a loose rein and you're hauling his mouth to get him under control, then I'd say back to longe work until he's balanced. Get him trotting and doing lots and lots of transitions w/o a rider (side reins and a training surcingle are great if you know how to use them loose enough to encourage stretching w/o being too tight to encourage leaning!), and get him to balance on his own. As he gets more muscled and balanced, then you can work under saddle.
When you do ride, start simple. Walk. Halt. Walk. Halt. Keep doing that until he's soft and responsive and will halt off of your SEAT and LEG aids and the reins become a simple soft accessory. Once that's accomplished add in trot, and bring him back to walk after literally just 2 - 4 strides of trot BEFORE he has a chance to rush and scoot forward and lean.
Sounds like overall your horse is on the forehand, and not balancing himself, and rushing and leaning due to a lack of balance. A harsher bit will just create more discomfort and not actually fix the problem, but create more as the horse tries to figure out how to lean/balance while also avoiding the painful metal object in his mouth - causing more rushing and leaning. I'm thrilled to hear that you're taking out the harsh bit(s) and also suggest going as SOFT as possible - especially a french link or a bean three piece, as many horses brace against a simple snaffle but learn to accept and salivate and reach for a three piece bit due to equine mouth conformation.
Good luck and please keep us posted on your progress. I'm sure that with a softer bit, some longing and balance exercises, and starting with simple walk halt transitions teaching him to respond to SEAT not HAND, you'll be back to trotting balanced. Until he's trotting balanced and can come back to the walk and halt with just seat and leg cues, I highly recommend against any attempt at cantering under saddle, as a horse needs to truly be moving independently of and balanced with the rider before they will be able to canter slowly and balanced.
I'm currently training a coming 4 year old for a client that's a clyde/tb cross and she can get heavy and lean. We're just barely doing canter work and only for very few strides as she learns to balance, and focusing on trot/walk transitions in the interim to build up muscling, topline, and self carriage. She's been in training with me since November of 2008, had been started under saddle before coming to me, and just now starting to begin canter work - on a very limited basis. Correct canter (and trot, and any under saddle work) takes time, so be patient! :)