Well my two Lugers have a very, very, very tiny amount of play there. And if I push the barrel/receiver away from the side plate the pistol still fires.
Unless there's an extreme amount of wear there I don't think this is your problem. You probably should have Lugerdoc do the trigger job for you.
The only other option would be to try many side plates until you find one that works reliably. Problem with that is where do you get your hands on a bunch of them! The ideal solution would be to find a matching number side plate that works reliably with your gun but how often do you get that lucky!
