The left and right shell stops work together when cycling the action. It sound like either one or both shell stops are damaged or need to be restaked. If you pull the trigger group out you can see the factory stakes to see if they are not holding. Hopefully you have a gunsmith that has a staking tool and they can restake the stops. I would still replace both stops if the gun has a high round count through it. A third possibly that happens when the trigger group pins are replaced for screws to hold on a side saddle. The shell stops can move rearward if the pins are too small causing a timing issue. I can’t tell if you have a side saddle on your shotgun, if you don’t and are using the factory trigger group pins, you can probably rule this third possibility out.
Interesting no answer to this but I may have a solution based on a problem I ran into while working my M3K over. Full disclosure, I just picked up my gun and tore it completely down for cleaning and adding some MOA precision parts to it. Anyway I stumbled on your question looking to see if anyone had the issue I was having. When swapping out the bolt release button and the shell stop or carrier latch extractor as the owners manual calls it, I found a short pin inside the carrier latch extractor spring that limits the travel. Why Stoeger added this is beyond me as it appears it’s not in the M3000. I started to practice quad loading and i couldn’t consistently get shells into the mag tube. The carrier latch extractor would lock up or not move far enough to let shells in even if I loaded singles. I removed that little pin and the problems are gone. Check to see if your gun has that pin in the carrier latch extractor spring. If it does I bet that’s your problem.