I think the video helps a lot! The thing that I notice the most, is that your hands are kind of busy. They move up with each stride, and I think you both would benefit from a steadier contact that doesn't bump his mouth. My trainer would put a grab strap across the front of my saddle for me to touch, so I would have a physical reminder when my hands were moving too much.
If the goal is training level, maybe its not an immediate need, but I think his trot looks nicer in the forwardness post-helicopter business. It gets more active and a little less on the forehand. I would do a ton of transitions to get everything more stable quicker, but it looks pretty good!