BP:
Boy, this is a tough one!  The surest way out of this mess is to remove the
head and take it to a shop with EDM ( electode discharge machining)
equipment.  Properly done, the original tapping may still be able to be used.
 Other than that, get some small grinding points, preferably diamond-coated,
and remove enough of the stud remnant to be able to get a grip on that
extractor.  Of course, do your best not to open up the mouth of the stud
hole.  Be mindful that Helicoils can atone for a multitude of sins.

This is tedious but, I know fronm experience that it is possible.  Good luck.
Rich