Broken Exhaust Manifold Stud

I was completing some work on my 89 Camry and noticed that the Stud is broken slightly below the edge of the head (so it appears with the Manifold in place).
Anyone have any success removing a broken stud without removing the Aluminum Head. Craftsman has some great looking Extractors.
I'm sure it was broken off when a repair shop did some work on the car (remove the head, to replace the Head Gasket) a few years ago and I just never noticed. Also notice the Exhaust Manifold has 2 cracks with exhaust gas escaping from the cracks.
THIS WAS NOT A GOOD DAY!!

Thanks for any ideas.

John

Also, if you think that it's sticking out far enough, you could always remove the manifold, and get some really good penetrant and coat it, grab yourself a pair of vice grips and get it out. I had to do that when I broke a head bolt not too long ago.

Unfortunately the stud has been broken off below the surface of the Head. If Toyota used something like Locktite when they install the stud into the Head, it could be a real pain getting it out!