If you try those craftsman extractors, and they dont work, you will be left with absolutely no edges to work with. It will just chew the livin shit out of the screw head, so make sure you try some other options first.
I have had more unsuccessful results with those extractors than good.
I agree with a combination of two previous posts:
Hose it down with PB blaster, and let it sit for a while. Hose it down again, and use an impact driver with the right size head.