"the trick is not to damage the slot......."

Listen to PA24, use a proper fitting bit, put it in drill chuck, lock down into the slot, acton in a vise, turn chuck by hand, just turn it a 1/4 turn to free the screw. You'll be surprised how easy it comes out then. You'll break the bit before breaking the screw. Get the screwdriver set from Brownell's with the thin bit set if you're going to work on SxSs.

The problem is most likely just 100 years of congealed grease & dirt.
Regards, Ron