Yay! It worked. I apologize for the quality of this video. To things to get for next week.. A tripod and a better audio track.
The quality is fine!! I could see you perfectly.
What's your goal with this horse? Will you be doing the all around? Or focusing on English? Western?
Getting that smooth, no head-tossing transition requires lots of work on your part. You need to push him into the bit which means taking a feel of his mouth and using your leg. Lots and lots of leg. Take it slow at first. Pretend like you're going to canter, and when he lifts his head, pull back and use your leg to get him back into frame. Do this over and over again until he figures out that you're going to check him back if he lifts his head. You might try using a running martingale to help you through this phase, too. Up to you.
I wouldn't work him on the rail anymore, either. He's really lazy through the shoulder. He could move tons better with some shoulder-in work or two-tracking across the diagonal. The trick is not to overbend. That can lead to those over-canted lopes that are so hideous to watch. Once again, take it slow. Bend for a step or two, and when he gives, release. Then do it again. And again.
You'll need to slow his canter down, too. You'd be fine at an open show with this canter, but not at a breed show. Work lots of circles. Spiral in--tightening up that circle--which will force him to slow down. When he's at the desired speed, spiral out. Working circles will help to keep your horse rounded and bent so that he uses himself instead of flattening out. A flat horse is a four-beating/tropping machine.
I'm sure you know you'll need a weighted tail. He carries his pretty high which takes away from the overall picture.