I'd actually suggest, for the jumping, because my mare does the same thing with her head, to always be sure to get in two point and give a release. You're riding very defensively (which is common with a quick horse, especially a head thrower), but they tend to do better if you give them their head over the jump because some of the head throwing comes from wanting their head over the jump. Also lots of sitting trot to jumps and then a nice easy halt on the other side, turn and jump in the other way, and keep going back and forth until your horse cools his jets. When you get back to jumping that is, because if he's anything like my mare he's going to be at mach 5 the moment he sees a jump and realizes he's going over it, and might even be flinging spit in your face with the head throwing
Also gymnastics or a simple ground pole in front and after the jump. This should be helpful: Slowing Down in Front of Jumps
As for your flat work, overall I would like to see more leg to push the horse into the bridle a little more to correct being behind the vertical. It might also help with some of the contact issues, although most of them seem to be fixes he still seemed a bit resistant in the test (in the video) and I think a little more leg with a quieter hand might aid in helping him find confidence in working into and staying in the bridle.
Overall he looks like a fabulous horse and I'm very sorry that he has been injured, and I'm glad he's getting better.