She needs more rein and I wouldn't move up gaits until she is more relaxed. You should teach her to take that bit and relax into the slight contact. You looked a little bit tight but much better than usual :)
Except madam that diagonal was perfect at first but you switched direction and picked up the incorrect one! Watch that.. the reason there are diagonals is so you can help your horse stretch those muscles properly and so we stay off of their back and help stay out of their way around turns.
But I'm being overly critical.. you did a wonderful job and continue to progress beautifully. Just give your mare a little slack and teach her how to relax. She doesn't need to be a peanut roller but head should be level to her back over time as that is where she can engage those back muscles and find her balance.
Also, she does have a naturally high headset, so I just let her go with it, I can be riding on loose rein and her head will be high like that, even when she's playing in the pasture, her head is up, never ever down.
She just that kind of horse I think :P but working the right muscles will most likely help her
If you let her "go with it" she's going to bulk up the underside of her neck and it'll be harder for her to keep that neck down and relaxed. But she has to learn how to do that. I would practice "giving" to the bit on the ground.
My horse is like this also.. but they never learn until you teach them how. Out in pasture doesn't mean they're comfortable with hollow backs and giraffe necks. I've noticed as my horse has learned to use his back more, he has begun to lose the giraffe headset out in the field :P
Kind of like how some people hunch and when you straighten them.. oh it feels weird but ahhh it feels better for their spine than how they were before. Yes it's more work but it's much nicer.