Broken bolt

Why not try an Easy Out screw extractor? It worked for me on an exhaust manifold bolt with poor access.
With the good access you have it should be straightforward.
My old high school shop teacher told me that there is no such thing as an easy out...........only hard outs :)
Use the thermostat housing to make a drilling jig out of 5/8 plate that locates from the undamaged hole and you will have no issue accurately center punching and drilling the offending hole.
I have a jig like that designed to drill out boken Hemi exhaust studs.