Damn the bad luck

Don't use an easy out! But then you knew that, didn't you? I agree with daredevil regarding the reverse drill bits. I've had success on other projects with them. The best way I've found to use them is to drill a small (1/8) pilot hole centered with a regular bit, then go up 2 or 3 sizes with the reverse bit. It will usually back the broken off bolt quite easily.
Good luck with it,
C