I would examine the heads carefully. If flat and not corroded, I would not skim. You don't need to remove the sprockets off the cams. You can remove the cam belt and lift the head off as is.
Well, let me put it this way. I have just done this on a K4 engine, and I cannot see any reason why this should not also apply to the KV6.
As for the head gaskets, I think the original gasket for the V6 is always multilayer metal!
The mayo should not be taken as coming from HGF, that is only one of three (four?) possibilities.
You can easily get mayo from leaking inlet gaskets and indeed also from a leaking oil cooler, and maybe (?) even if the internal ventilation system is not maintained and blocked.
I would not jump to conclusions based on what you have stated here.
As for the thermostat! well................, what can I say