To reprime, use a wooden dowel in a drill press, with the primer on a block of wood that is drilled slightly to cup the anvil and not the primer. If you push a shotgun primer out, it's a large rifle primer inside an anvil.
I deprime with the drill press and a pin punch, with the case centered over a hole in a board.
Use standard shot wads and loading, pressed in with the wooden dowel. Use an overshot card, and cut off the crimp, seal with hot glue.
If the shell came out of the gun, it should reload in the same gun without sizing, unless the chamber is out of round...unlikely...all mine have done fine.
In truth, 20 ga. and 12 ga. are relatively reasonably priced, 410 hurts my feelings somewhat....I began experimenting with loading for that reason.
Use a load manual, correct components and powder and be careful...
Ben