Been there.

Sears screw extractor?
The metal in the screws is too hard to get a bite and it works like a drillbit.

Drilling off the head?
My screws were rusted/in so tight that the welded nuts on the backside broke loose, that would be fun with vise grips.

I hindsight, I'd try penetrating oit and hammering the correct bit as deeply in as you can or if that fails easy out.