Screw Stuck in Phone

One solution could be to apply a really small amount of superstrong glue to a really cheap screwdriver, just like the ones you get when you buy a screen on ebay, and put it into the screw until the glue has hardened. Then you may be able to get it out, and just have to replace the screw. Do NOT apply the glue to the screw itself, because you could be unlucky and fasten it even better.

Another extreme idea, if there really is no chance of screwing it out, you could drill a hole in the screw, with a drill that is thin enough to get only the head of the screw of. Then later you would only be able to get one screw to fasten it when you are done, but that should be enough. The battery connector normally will stay on anyway.