Hmmm, yes even Astro physics focusors can and do move Bert.
I am convinced though that if you sort the flexure related issue in the way described the very minor elongations in the corners or edge of field will be barely noticable.
I have considered this problem quite a lot and yes while an F3 is problematic it must surely be solvable but I do think not by the methods you are currently employing. The optical system and camera system you have bought should not need this method of control. Each are solidly constructed with screw thread design and therefore not likely to move. Mike's system is more likely to move than your system. I am more inclined to think your flexure is coming from the side by side bar system, refractor and the guide camera connections rather than the RHA and FLI gear. That is my considered option. And well thought through.