Until you find the correct muscles to hold with, I think you’ll find this to be a difficult battle. The trick is that the body really must be soft and fluid feeling, with positive tension and alignment. If you try to hold yourself in place, you will only add to the tension, particularly on a sensitive horse.
I would highly recommend doing yoga or Qi Jong to find the idea of being centered, elongated, aligned and strong while simultaneously being soft. Thing of yourself as a dancer rather than a gymnast. Riding is about feel - raw power and strength often works against us.
What I see in your riding is that you are too strong in the wrong places, and all the tension in the wrong places is causing you to give in the wrong places. The core and back should be strong, whereas yours give. The hips and ankles should be soft so that the leg can cling, but yours are tight.
I would first work on just relaxing, feeling, riding, softening, get a bit messy, let that leg soften up, and then as you’re doing that well, begin to start thinking about drawing the upper body up toward the sky, pushing the bottom back in saddle, so that the hip can softly fold.
A specific exercise for your upper body issue is to take a whip - a jumper bat works best - and tuck it into the front of your breeches so that at rest it taps your nose or chin (a short crop will not be as effective, or at least as motivating, and you won’t want it so long that it will poke your eyes out). When you are centered, aligned and have the correct muscles engaged, the whip will point forward and out over your horse’s ears. But when you give and collapse in the middle, it will come back and whap you in the face. You want to think about relaxing and simultaneously pushing the whip away from you. Try this on the ground first and then do it mounted. This is one of my favorites from Greg Best.