If you are using that shotgun for wingshooting or clays, you are better off without a bead on your shotgun. Many coaches for clay shooting will actually remove beads for beginners. You should NOT be looking at the barrel when shooting at moving targets. Shooting turkeys is different.
So, to your question: I'm trying to figure out what is actually the problem. Are you saying the bead's threaded post has protruded through the barrel into the bore? Did you drill that hole? Stevens should not have drilled through the barrel. Is this a home defense cut down the barrel affair? Doubtful since you think it's full choke but if so, then again no need for a bead on a door crasher so just get rid of it. To trim down the bead post you could use a rattail (round) file. I wouldn't worry too much about scratches in the bore. Those shotguns were little more than a club right out of the factory. You won't be hurting the resale value. Because they don't have any resale value. A few scratches won't hurt the full choke. Just use care. A Dremel tool with a narrow grinding wheel bit would be ideal but I'm thinking you probably don't have one.