If you have clear access to the head, this method will work, but it requires care.
You need a little spiral tool for removing stripped screws. Not one of those Sears things, Easyouts or whatever they call them, that have two biting edges. All those are good for is removing larger amounts of metal. The tool I am referring to has been around a lot longer, and looks sort of like a softserve ice-cream cone. The one you get needs to be smaller than the shank of the screw you're removing. If you don't have small drill bits get one of those at the same time. The person at the hardware counter can advise on matching the bit to the screw remover.
Now use the drill and drill into the center of the screw head. Drill in about 1/4" if you can.
Once you have the hole drilled you will be able to insert the remover, which is spiraled to bite when turned counterclockwise. The screw will come out.