Well, I don't think I can necessarily stay within the boundaries of what you requested for a critique. You grabbing the mane is based on not being really secure, and that is based on not having your leg under you, primarily.
Is that a jumping saddle you are in? it looks like the stirrup is a bit long, and your leg is out in front of you. I do not see your weight down through your lower leg. It looks like you are riding more off of your knee, which means that your lower leg is not acting as the very strong support that itneeds to be for you to feel secure about the jump.
When your leg is out in front of you, it means that you are always a bit behind the motion. I think this is maybe why you end up bopping hm in the mouth a bit, and it looks like you aren't always certain when to move up on him, I mean you tend to jump "for" him, rather than having him lift you up and over.
Have you ever done any jumping on a lunge line, without any reins at all? Can you ride your beautiful horse over a series of ground poles in two point? on a loose rein?
Once you have that leg more under you and more connected with weight goind down through it, I think you will feel a world of difference. Your horse is a total doll and you are well suited to him.