Dennis - welcome - sounds as if the musket nipple is too long. Chuck it up in hour electric drill, holding it by the threads or boss, drill held in a bench vise (if you don't have access to a lathe), and with the drill running use a fine file to shorten and true up the top surface.
If the top surface is peened, blunted on one side as you noted from dry firing, it will make the cap difficult to push on, or perhaps difficult to remove.
Perhaps it is easiest to just replace the nipple. trackofthewolf among other places, sells them.