I also have a TB who tends to be stiff to one side. Here's a few things I've done to help him bend around my inside leg better.
1. Shallow serpentines at the walk, just enough to create flexion to unlock his poll and jaw. These are to be done from seat alone. Just weight your inside seatbone and put it slightly forward and your horse should bend in that direction. Use reins only as a reinforcement if necessary. As soon as you see his inside eye or feel him soften, time to go the other way.
2. This one's more from the western world but works GREAT! It's kind of like leg yielding in circles. Drop your outside aids completely. Using you inside rein, ask him to bring his head to your hip. At the same time, use your inside leg to keep "forward" motion. Basically the forward will result in going in circles since you're directing his head toward your hip. It's a slow give and take exercise. As soon as you get any result, reward him by letting him move forward and straight and then do the same thing on the other rein. Once he gets what you're asking for, you can ask for more bend of his neck. With each new attempt, you should feel him soften a bit more.
3. Assuming #2 worked, try leg yeilding in a stair step pattern. 5 steps leg yeild, 5 forward, 5 yeild the other way, etc. Make sure you have a slight flexion to the opposite of where you're heading.
4. Best way I know of to strenghten that inside leg is to do shoulder fore or shoulder in. My TB can only do a few steps at a time in his weak direction, but we're getting there.
5. If any of the above have produced softness, try some basic patterns, large circles, serpentines, anything that keeps him in a natural bend. Even on a straight line, you want a little flexion to the inside. Without bend, he'll be stiff as a board no matter what you do. Make sure your inside leg has soft, inviting contact or he won't want to bend around it anyway. Good luck.