I'm going to guess dressage is your goal, but if not, then my bad, lol.
The first thing I see, is so lazy! His hind end almost looks like it's stopping every stride anticipating to walk, then realizes "nope, not this stride!" and catches up. A good thing to work on in my opinion, is in-gait speed transitions, especially at shows its important to have immediate responses so you can fix problems before they tank your score. Say, during a shoulder in, he starts to get lazy and behind your leg; you want to be able to immediately lengthen his strides and make the judge think that was just one bad step at the beginning. So, in the trot, really push his trot to the max extension, really stretching his legs, then bring his back like a coiled spring to an exaggerated collected trot really activating his hind end, and send him back out, and repeat like he's an accordion. Make really extreme differences within the trot, and play with how long your in each speed. When he's really sharp, you can get him to the point where you can almost do a stride or two of each with smooth in-gait transitions (at the canter, push him to a real ground covering gallop, then back to cantering on the spot, no quitting! And repeat). Do this at all gaits, all the time, its real helpful with a lot of problems.
I'm not real sure what your goal is with cantering him for a few strides at a time, I think that makes his laziness worse. Other exercises, circles, leg yields, work on cleaner down transitions. Maybe some circles, starting with 20m and spiraling him down to 10m by pushing him away from your outside leg, spiraling back out to 20m pushing off the inside.
He looks pretty cute though, so fluffy compared to your profile picture! Good luck.