Well, earlier he said the HG is OK since it was replaced not long ago... Now it's not OK because ???

If he's removing the head, resurfacing, (maybe resurfacing the block too??) that explains the high cost.

I can't see the engine firsthand, your mechanic CAN. There's some amount of sooty water that's normal in the exhaust, especially when the engine's cold. I can't see how much is there, to compare against what I think is 'normal'. When it's running & spitting sooty water, does the exhaust smell sweet like antifreeze?

You say your mechanic's reliable, and I'll say a warped head after overheating is certainly possible... If you feel like doubting him, there's ways to test. For example the antifreeze can be tested for combustion gases. Or you can get a leakdown test.