This is my guess as well. Vibration and heat are your friends, but worried about that Al cover. Maybe turn the air hammer WAY down and gently vibrate while prying. Apply heat at the broken bolt to get the Al to expand.

Would be nice to have a second person

Those water passage bolts just go back into air space, so no worries about drilling through anything if only there weren't a broken extractor in the way....

 

I just grab it with vice grips, liberally apply some chemicals, then tap the end of the bolt lightly with a hammer, while applying a bit of torque to it. Once it breaks loose, like can thread it out with your fingers.