I think he would be a very nice horse to take you through 3rd. His gaits aren't huge but he isn't being asked to go forward in the video - rather, he is being presented in a hunter fashion. There's certainly more in there
With correct training and riding, I've no doubt he would get you where you want to go, provided his mind is willing, and he looks like a happy mellow sort. But I'd like to see someone like your trainer ride him to see how he responds to being asked for more - more walk, more trot, etc.
(MUCH better than the draft mare, BTW)