I agree, transitions, trot work over poles and up hills, canter work in a lowered frame (but still moving out from behind), and some belly lifts!
Do 2 belly lifts on each side before and after your ride. Use your finger tips/nails and push up in the center of his belly (you'll see a mid-line under there, and a "soft" slightly swirly spot). Push up hard until you see his back arch. If it doesn't work, move around to a different spot, or look under to make sure you're on the mid-line. If he still resists, use the curved part of a hoof pick (not the pointy end).
Trotting over poles and canter work really helps, IME, the most. Work on a big circle at the canter, going from true bend to counter bend in a lowered frame. Hold the counter bend until he relaxes, then back to true bend. This will work his topline and his underline. Building topline will help support his belly and make for a more athletic horse. Work him in a lowered frame, encouraging him low, not forcing him, but keep his gaits ground covering and moving out. If he slows down too much, he can topple on his forehand and get strung out behind, which will have the opposite results.
Do you have a Dressage trainer near you? Some Dressage lessons might come in handy for you. They will teach you better balance in your saddle too, no matter what kind of saddle you're using.