The drill press (or milling machine) method to back a stubborn screw out is about the best. It allows the great downward force on the bit to be maintained so it doesn't twist out of the screw slot,,while you carefully turn the chuck by hand to back the screw out.
Lock the gun/part in the table vise securely or clamp to the table to avoid it moving while doing this or you risk the bit slipping from the screw head and marring the finish.
Another trick if you're just using a screw driver free-hand on the screw with the gun in a bench vise,,with a close fitting screw driver blade which you should have anyway,,put a tiny touch of grit on the blade before you place it into the screw slot.
I use valve grinding compound or rosin 'cause I have both handy. I'm sure there's other materials more gunsmith PC.
But the idea is the same,,it gives the blade a good bite & grip in the screw slot and helps avoid the blade twisting itself out of the slot as it's turned.
Heavy downward pressure is the key, which is why the drill press trick works so well..
Don't be surprised if you break a bit or two using the drill press method before the screw finally comes free. Especially if the screw is the really fine slotted type.
At least you have control using this method and you won't damage anything on the gun.
You can also put heat on the screw w/an electric soldering gun. Just the soldering tip placed on the screw head and heat it up.
The little circuit board soldering units will do for the small screws,,a pistol grip type will heat up larger screws quickly.
Cover the soldering tip with a twist of aluminum foil if it's tinned and crusty from soldering work. That'll avoid any discoloration to the blued screw. The heat will transfer just fine.
Loctite, solder, stock finish, crazy-glue are all possibilitys as a thread locker. Heat will defeat them all. Some will need 400+F,,most less.
Patience, and don't damage that screw slot, or you'll have to drill the thing out.