I'm trying to take off the shifter to repair it, but the head of one of the screws is stripped. I've drilled a hole into the screw and have tried to use a screw extractor but it won't budge at all. The screw seems to frozen in there. The other screw came off without a problem. And with the head of the screw not being exposed, I can't cut slits into it to try to make a phillips fit or to use a chisel. Any suggestions would be greatly appreciated.

Thanks