Make sure that your cues for canter and your cues for a bigger trot are different. You said she rides more from your seat than your hand, so make sure that you are asking for more trot and keeping your seat consistent. Make the trot seat and the canter seat very different.
I have an OTT TB too, and they *all* do this, so it's not just you... I doubt that makes it less frustrating though when you spend 20 minutes in the walk each ride! :)
Bailey does the same thing when we canter, suddenly every cue means canter. there is no possible way we can walk calmly after that. To fix it I had to go through a lot of "bad" rides before he actually understood that just because we cantered it doesnt mean that we will canter for the rest of our lives. I would canter early on in the ride, that way when he acted up about it I still had enough time left in my ride that he didnt get cranky and I didnt get as frustrated. I would bring him back to the walk immediately after the canter, and really loosen my reins.
yes, I said drop my reins. :) track TBs are taught to lean into rein pressure and I dont think that with any amount of training they ever totally forget it. I keep a loop in my reins, if he gets quick I use a half halt with my seat to slow him, if he doesnt respond, a quick tug with my reins. I make sure my seat is swinging the rhythm I want, not following him. Eventually (sometimes 20 minutes) later, he would walk calmly. Now it only takes 2 or 3 mins. :)
Another idea that really helped was to put him to work in the walk not just let him lolligag around. If I worked on bending or flexing he got distracted from the canter work and focused for me. TBs usually are very willing and actually try too hard when asked to work, so some of the problem may come from wanting to keep working. Most people ride the walk very loose and let the horse sort of wander. If you put them to work it keeps them focused.
Same when you transition from canter to trot, start to figure eight and ask for bend changes, and once you establish a steady even trot ask her to lengthen and shorten her stride every half circle to keep her focused.
"The white horse moved like a dancer, which is not surprising: a horse is a beautiful animal, but it is perhaps most remarkable because it moves as if it always hears music."