To me, it looks like he’s done with your shenanigans. You look like you are riding with your hands and not seat and leg. He was good for the trial rides because he had good training and that was your first couple of rides with his previous owner likely riding in between to reinforce his job. Being better at the beginning of a lesson and degrading into what that second video showed is likely because he’s ever hopeful you will learn to stay out of his mouth.
In the first video, in the entire video, you looked to me like you were hanging on his mouth a lot. This was especially prevalent at the end when you were trotting across the field with a tight rein that was shorter than it was earlier in the cross country school and you did not seem to let up at all over the small jump.
In the second video, even at the beginning while the reins were longer, you were fussing with his head the entire time like you were trying to bring it down/in something of a frame. It got worse as the video went on. That jump he could walk over and you two should have walked up to it on a loose rein and let him chill at it. Changing to a tougher bit isn’t helping the situation.
I would see issues like this when I used to work with finding new homes for thoroughbreds off the track. It was invariably someone used to a quarter horse/lesson horse type who put way to much leg on the horse then freaked out when the horse took off and responded with hanging on the horse’s mouth. The head tossing is, to me, an indicator of this horse’s annoyance. Going over a jump and hanging on the horse’s mouth means the horse feels it cannot balance well to get over the jump. No matter how bad a horse is rushing, I have learned that one to two strides out, just let go. I either abort mission or just let go, but previous to that if you are doing your half halt correctly, you are using more seat and leg than hand and settling the horse that way.
Personally, I would go back to the snaffle and go back to flat work until you can at least speed up/slow down the gait, if not drop down/go up gaits without touching the reins, as well as the ability to at least turn the horse if not do a full circle without touching the reins.
If you can do this on the flat and these issues just appear when jumping - get a neckstrap or grab mane and start with ground poles, set your hand so there is a loop in the rein at least two strides from the “jump” and after. Start with walk, then trot, then canter and once you can do ground poles well, start moving up.
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