I've been in this situation when I was a Mechanic. I eventually used a hammer screwdriver. It works by hitting the round end of the screwdriver, and the internals use the force of the hammer to shove the screwdriver bit as deep into the slot as possible, and transferring half of the force to turning the bit. I sold all my tools years ago, but maybe someone here, close to you, (you don't indicate where you are) has one they could lend you or help you. Any Gunsmith would have one too. The whole kit is a bit expensive if it's just one screw that's giving you trouble, but there's nothing else like it. Dribble some WD-40 on the screw first.
