Broken bolt

All,
I was working on my Ambassador and one of the bolts on the gooseneck broke off. I tried everything to free it including left handed bits but all i am doing is breaking bits. Have broken 6 already and cannot get deep enough to try to get an extraction bit on it. Any ideas? Welding is not an option.

Take the manifold off and i might as well just get another manifold bec i still dont see how it can be removed without damaging the threads.

Lot of work for a thermostat.
Author: mdh157