I had a similar 'oh s**t moment a couple of months ago and did the same as Trebus suggested.
Drill out the center of the screw (fairly easy as the hole is already there) as close as you dare to the diameter of the inside of the thread, using good quality carbon steel drill bits. I managed to get the remainder out without doing too much damage to the thread in the caliper by levering with a very small screwdriver. Very satisfying (and relieving) when it finally comes free!! I also had the caliper in a vice to keep it steady while working on it.
I replaced both of the rear and front bleed screws with stainless ones to try to avoid the problem in the future. Hope you have success too!