Also, if you're any good with a soldering iron you could solder a flat piece of brass (like maybe half of a brass washer) upright to the screw head, then grab it with a pliers to back it out.

I had a tiny bolt (these really are small, usually take a 000 phillips, maybe 2.5mm) holding on the back of a MacBookPro refuse to come out, I tried the smallest of these without success, but it took the head off and I was able to remove the back cover. Even then, the stub of the bolt could not be extracted, so I just ground it down with a Dremel.