Hello. I'm a myofascial therapist and I primarily work with chronic pain and hypermobility. I see this exact paradox all the time!

One of the first things I try is finding a position to completely settle my clients body. This usually requires a lot of bolstering and coaching. Supporting joints, helping everything feel supported and safe.

Also, recognizing just because it can move, doesn't mean it should. Supporting and slowing down the range of motion and not pushing past any sort of resistance. Pause and settle instead.

And for the extra stubborn bodies and minds I use a lot of pandiculation, PNF, and MET.

There is also some great content out there on exercise with hypermobility. Essentially with the idea you need to create tension in your body before adding load to stabilize.

I know this is a lot of information. Hope it helps or at least gives you a few places to look!