1984 Pontiac Fiero 4 cylinder with a broken head

Engine Mechanical problem
1984 Pontiac Fiero 4 cyl Two Wheel Drive Automatic

What I thought was going to be a quick head gasket change has suddenly turned south.
A head bolt broke off and has so much carbon built up around it that I cant get the head off.
I had the car lifted off of the ground by pulling up on the head with my engine hoist.

The bolt in question is the center bolt on the exhaust side of the head.
It is centered between a pair of siamesed exhaust ports, probably the spot where there has been the most thermal expansion anywhere on the head.
I suspect the repetitive expansion is what allowed the carbon to be so tightly compressed.

The head of the bolt and about 1/2inch of the shaft broke off before I had rotated it 1/4 turn.
This makes me feel the shaft of the bolt is froze in place, as I would have felt a flex or torquing of the shaft if the problem was just the treads in the block.

So I have about a 2 inch length of shaft. 10mm in diameter, in a 12mm hole. With carbon built up around it, packed very tight.

These bolts are metric grade 11.9 which is harder than SAE grade 8, so drilling will be difficult to say the least, not to mention trying to keep it centered and straight.

I feel that I will be able to remove the bolt easily, after the head is off.

Any suggestions of how I can pull the head off of the bolt?