I don’t know if this is going to answer your question but I will share my experience.
I have started GTG almost 3 months ago with regular push ups (my regular push max was 12). Then I have moved to One Arm Push Up on counter top, I was feeling that rotation and was not stable at all! I was really a bit shaken cause I thought to get strong enough might take very long, but in a very short period, I became stable (I used full body tension hardstyle as much as I can)
My next progression availability at home was quite difficult for me so I have decided to do one arm, one leg counter top.
The first few days, the twist was so bad that, I said I will not be able to correct this.
But booom! I have became stable very quickly.
So my guess, at least in my case, my nervous system was not used to rotation and was not able to fire muscles. Once my nervous system “understood” what should be done, stabilization came very fast.
I am writing this to encourage you.
My stabilization of the twist came very quickly relative to any other strength skill. For example, I have tried sternum chinup for some time, and failed to improve quickly(now did not give up, but working on hangs and hang drills, gtg style I will come back to that one again)
Full body tension and a bit of patience worked for me.
GTG also clearly made my joints stronger and my joints feel much better. I don’t go in to a lot detail, because it might be bad example for some, cause I haven’t follow health recommendations. But bottom line, my joints became pain free and stronger clearly as a result of GTG.