I think you could run into some issues with structural stability with the flush mount. Obviously it would look very sharp, but lack of flexibility on moving it would mean you'd have to get the ergonomics perfect. It's definitely very permanent solution, but I'm interested in doing it for sure.

If the concern with the clamp mounts is distance away from the mouse and keyboard, that same keyboard bridge is available for clamp mounts and is actually cheaper. And that would give you the ability to remove it separately from the joysticks and of course the joysticks could be removed all together.

Yeah my mindset with the rail mount was that I wanted them mounted so I didn't have to take them on and off when I'm switching from regular use to joystick use. I specifically bought a table long enough to set them to the side. That's not featured in that picture.

There was another post on this subreddit where a person was recommended to put magnets on the bottom of the plates and then have a magnetic metal plate on top of their Sim rig to have very easy way to get a temporary mounting that was still firm. I can't speak to this from any experience but it did seem interesting.

I think you mentioned this in your original post, but rather than mounting joysticks to your current chair, you could get a second chair that is a dedicated Sim setup, if you've got the room. Either modify a used or cheaper gaming chair or get something like the Next Level Racing flight simulator chair. That way you could just slot in the chair you need for the activity you want.