You need to watch some Youtube videos from Art2Ride. The instructor is Will Faerber and he is all about how to build the topline of your horse to make it possible for him to do the athletic movements that you require.
It’s all about stretching the horse long and low, down into a contact with the light rein, while keeping his back legs active and pushing. It takes time. It doesn’t happen overnight.
He has many video critiques that he’s published helping people who are working on their own. With this work, over time you see the back come up and fill the dips in front of and behind the saddle.
I’ve used his advice to build the strength to do the more collected gaits at Second Level. It worked for my horse and his back is NEVER sore.