[ithacaartist]

Support the body of the side plate in a padded vise with tang sticking up to receive the tapping (also with something non-marring). Tap the tang in the direction that would tweek the front end of it away from the frame. This works to take up the play in the side plate by leverage. The pivot point is the front edge of the side plate's body. Raising the front end of the tang makes the back end of the side plate rise more when the locking bolt is swiveled over to lock things down, snugging the small flange on the back end of the side plate body more firmly into its slot in the frame, directly behind the side plate.

Strictly speaking, your side plate will be .018 out of parallel with the frame; or it may actually end up exactly parallel, since you have adjusted it back to its original position. Regardless, you will have no looseness whatsoever when you are done. The disappearance and reappearance of the problem after shooting some rounds...? Sure, a gun heats up a little after 4-5 mags, one right after the other, but I can't see this affecting the side plate. If the issue goes away and comes back, unconnected with any adjustment, then I'm stumped. If so, perhaps there is some mechanical instability with the assembly that is not obvious--maybe something amiss with the fit of the side plate flange in its relieved area on the frame?

Don't worry about bending SS and breaking it. It is 'tougher" than carbon steel, not harder. It displays more "spring back" than carbon steel, and usually needs more displacement in bending to wind up in its new shape/angle/whatever. It will eventually stress break, but will generally endure back and forth bending significantly better than carbon steel. The slight bending of the material involved in these adjustments, coupled with the material's resiliency and the infrequency of bending applied, will reduce the likelihood of breakage to near nil.

I hope this is clearer...