Broken manifold stud in head

Tried to remove it with a bolt extractor and of course the extractor snapped - so i now i have 2 broken pieces in the head. :cry:

Bought a carbide bit but it doesn't even touch the hardened extractor - but i did have some luck grinding it down a bit with some abrasive bits that came with my dremel tool. So here's my question: do I continue to grind it down with abrasive bits or should i try a titanium drill bit? Can anyone recommend an abrasive type that can do the work?

Engine is assembled but out of the car so i can get to the hole easily.

thanks for the suggestions