I'd love to have your seat! you sit very nicely, have a really nice , long draping leg ( a bit too long, perhaps), and are very "sympathetic" in how well you follow the motions and absorb some of the rough transitions. you are very easy on your horse, and he appreciates that. I can see that he did better going right than left, which might have been a product of having warmed up more. he looked a bit 'trippy' at first, and I saw some instances where he appeared to lean on the nice steady and sympathetic hand you offered.
that's a bit of the problem. you are getting some nice forward, and getting along nicely with him and everyone's having a good time. but, the next thing is asking him to put his head in the game a bit more.
to me, that means, not just fall forward, STEP forward. not just back up, back up with energy and thinking, not just canter, but canter with spring.
now, I always have to preface these things with a disclaimer; I can't ride nearly as well as you. not nearly. But, I can see that as Sky said, you need to start putting in more half halts, once he is wamed up, and ask him to soften, not lean on that reain, and step up and carry his own head, and be resonsible for his front feet.
to do that, you need a bit more anchoring in your core. shorten your stirrup one noch. still a long leg, but NO toe pointing down fishing. your stirrup, while not something to stand on, does serve a purpose to help you keep a bit of bend in your leg, and this helps you to have more adhesive surface and a better centering in your core to counter the forward pull of the horse. it will also dampen a bit of the very slight "pumping" I see when you are trying to shove him forward a bit. SUCK him forward, with your core.
and be relentless in keeping your thumbs on top. it matters.