You can do some cavaletti with him... getting him to reach forward with his hind legs to go through them.
Also, just starting each ride by lots of long trotting forward. Push him forward with your leg and have a contact with your reins but dont necessarily hold him back when he gets quick. The idea is to speed up the hind legs, and once you have them moving, slow the front legs. He will lift off his forehand, push under with his hind legs and use his back. It's the basis we use in changing a horse from a different dicipline (mostly OTT or hunters) into dressage, which requires lots of hindend push.
Most likely its from his race training, as most OTT TB's are very on the forehand. Most TB naturally are weaker in the hind end anyway, so building the muscles up is a lot of work.
Lots of hills will help to correct that, once he is strong behind the push will come easier. But the understanding of putting on your leg means push from behind and lighten in the front will come from just driving him forward at the start of each ride. It may take a little time, but suddenly he will get lazy and slow and his tempo will even out. Keep your leg on to reiterate the point.
Also lift your hands a little as you ride, make sure you sit nice and tall and straight (even if youre riding huntseat, avoid perching forward in a normal hunt seat, sit back more so that he can lift off the front end easier).
"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."