I don't think a lack of go is the problem here. I captured the picture below, and will delete it in a couple of weeks, but here is where I suspect the problem with the 'go' is:
There is enough stiffness in the leg and back that you cannot move with
your horse. A chair seat can work, but only if you flex a bunch with the lower back and hip. If you brace at all, then that position results in you hammering the horse's loins. And the horse responds by saying, "Why should I shift gears if I'm going to get punished for it?" At least, that is how my
horses respond...don't ask me how I know!
The second problem is your reins are saying slow, so what is it you really want him to do - go slower, or faster? You can loosen the reins and still steer with them. It might be tight on one side, but tight on both sides tells most horses to slow down. It doesn't seem fair to use a crop on a horse when you are already pulling on the reins.
I got the same impression from the "Posting at the trot in English" video. If I wanted Mia to throw me, that would be a good combo - ask her to go faster while keeping tension in the reins. And if I used a crop (I actually use a leather rein strap on the very rare times Mia has a broken 'go-er'...usually it is her 'whoa-er' that is broke)...she'd buck, and buck hard.
Might be good to work on turns and stops and transitions and balance at a walk and trot. I think your horse has too much food on the plate to digest it all well.
Just my thoughts. I'm a nobody rider, so just FWIW...