Like almost all shotguns, the 870 shells latches each serve a separate part of the feed cycle.
As above, when the pump handle is pulled to the rear, the left action bar presses the left shell stop out toward the inner receiver wall and releases a shell into the action.
When the pump handle is pushed forward, the right action bar presses the right shell stop outward against that receiver wall and allows the next shell in the magazine to move a short distance to the rear until it's caught by the left stop.
Each shell stop has a slightly different bend on the front that contacts the shell head.
It sounds like one of the shell stops is defective.
Again, either find a local gunsmith who knows how to replace the 870 shell stops AND who has the special staking tool needed to do the job, or send the stripped action in to Remington for repair.