Check the action bars to insure they're not bent in or out, or up or down, or are kinked.
You can use a straight edge to check the bars on the top or bottom side and on the outside or inside for bends. In order to cause your problem the bars would have to be in really bad shape.
Check the activating bevels on the bars for burrs, damage, or excess wear.
The bevels are the small "ramps" on the action bars that activate the shell stops.
The 870 action bars and shell stops are not a complicated system.
When the forearm is slid to the rear, the left action bar ramp presses the left shell stop out and allows a shell to be pushed back into the receiver.
As the forearm is pushed forward, the right action bar ramp presses the right shell stop out to allow the next shell to slide back and be caught against the left shell stop in the next to feed position.
Remove the entire trigger unit and take the gun out to a safe place.
Load a single shell into the magazine pushing it all the way in past both shell stops, and slowly operate the forearm, watching the interaction of the shell stops as the shell is fed.
Then load two shells and operate the action again.
You should be able to see how the system works and any problems with the shell stops failing to retain the shells properly.