Never had a problem like you describe, but our policy prohibits us from loading less lethal into any of our regular service shotguns. Our less lethal only goes into our old Ithaca Model 37s with bright green furniture. The Model 37's don't have a floorplate so we don't have the same type of issues that can happen with a Remington 870. Even without the loading issues, I would suggest setting aside a less lethal weapon and putting distinctive markings on it.
Death is lighter than a feather, while duty is heavier than a mountain.