First off many of these American variants are A&D copies "Only" in the fact they are Box Locks & are not direct copies. Box Lock guns were in use prior to the A&D patents,even back into the flint era, so every Box Lock is not automatically an A&D copy. "IF" you want to spread it that broad then every wheel in existence is a copy of the original wheel.
I think it best just to say the A&D is the most copied firearm in existence & leave it at that. There are many mechanical mechanisms which have been widely copied other than the simple ones illustrated. What about windshield wipers for instance.
While I don't have exact numbers for either I Very Highly suspect that Singer's Oscillating Shuttle, Ccentral Bobbin sewing machine has been copied in greater numbers than has the A&D shotgun. It debuted in the 1880's & is still being copied & produced today.