Wow La Mojo, Looks like you might be able to get a bite on that screw with a pair of needle nose vise grips. They make a pair of really small ones. If not you'll need to carefully remove the head with a dremel, soak with penetrant then remove the body. Then you can deal with the remainder of the screw.
I would use the drill as a last resort. My .02$ Good Luck.
Paul B
