So, he picked up the right lead because you tugged on the right rein right before the jump in an attempt to get him straight at the jump. If you watch the video closely you'll notice that all you did was turn his head, for the most part, and dictate which lead he was going to land on. He popped his left shoulder out, making him land on his right leg first, thus picking up the right lead.
I'd like to see you coming to this jump in a lot more of a frame, not with his head in the air, even as a green bean you should be introducing and enforcing the etiquette you desire (to a lesser degree) and that will be required of him when he is more seasoned. Circles are not demonic torture devices, get him working over his back before even approaching the jump, also, I wouldn't be working on a long diagonal single as that is one of the most challenging thing for a horse to jump, they WILL build up to it, they WILL want to charge at it.
Try a jump on a big circle, get him working over his back on the circle over a ground pole. When he stops getting worked up over the ground pole, make it a cross rail. When he calms down over that, make it a low vertical. You can even make him focus by changing directions of the circle. Straight lines are easy to build up momentum. I also spend a lot of time trotting back and forth over something. Trot up, jump, halt, turn on the forehand or haunches, trot, jump, halt, etc. until my horse gets the picture that it's nothing to get worked up over. Repetition is really the key when it comes to an excited jumper.