It's a throw away the stock ASA mate get a cp ASA or a on off ASA
really?!
whilst I concur that an on/off ASA would be a better upgrade, you haven't really addressed how to help Cornelius fix the problem.
If it's not the rail grip grub screw, then it's the actual rail itself.
Basically, you will need to pull off the stock ASA entirely to reveal the rail itself. The rail is secured by 2x hex screws on the underside of the UL grip frame. Tighten the sh*t out of these to prevent further wobble. Reattach ASA and secure in place by tightening the rail grip grub screw (IMPORTANT: do not over-tighten this grub screw as you will potentially pop its collar off the UL frame and that's a whole can of worms you don't want open!).