How does one remove a rounded bolt?

I have a rounded bolt in a front brake caliper. The first
came out after some breaker bar persuasion, however, this
one tossed the socket until two corners were gone (pb
blaster had been well applied prior). I have an extractor
set, the largest socket was too small by 1 and so after a
few other attempts I used a dremel to grind the head down
to a size that would accommodate, attempting to maintain
the hex shape. Despite the extractor now fitting on snugly,
it refuses to grab and slips impotently off. I also attempted
the insert type of extractor, that broke off in the hole I
drilled for it on the first turn. Any advice?