New answers tagged screws
That screw seems to have found the magic spot and I think it's unlikely to happen again, however you might want to somehow strap a protection plate around the Tee; I wouldn't worry about the rest of the pipe.
Somewhat late to the party but a good solution I've just used goes as follows: Buy some reasonably thick dowel (say, 10mm) and cut a length for each existing screw hole. I'd suggest the length of the screw you are using (plus about 25% extra if your door is not solid wood). Sand one end back square - this is the end that will be exposed when the dowel is ...
If the head is readily accessible you can use a fine toothed metal saw to cut a groove with which you then can use a regular flat screwdriver to unscrew.
Use a hand plier to apply on screw head and rotate
I usually just cut a slot in the screw head with a Dremel or similar rotary cuttter, and then use a regular screwdriver to unscrew.
You may have some luck with a screw extractor. They come in various styles - here are two of them: The extractors are designed to screw themselves down into the head of the screw while at the same time applying torque on the screw in the direction that would loosen the screw. Your described screw had a hex socket type hole so the extractor may be ready ...
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