Got to be worth flushing it with something pretty aggressive. If it has, as you suspect, had some nasty additive in the cooling system it could have blocked some of the coolant holes in the HG. Some of these are pretty small to control coolant flow for even cooling. If they are blocked they will restrict coolant flow to parts of the engine, and reduce overall coolant flow, perhaps to a level that would result in the overheating you are seeing.
As it is misbehaving mainly when given a hammering, when demand on the cooling system is greatest, this would tally with what you are experiencing.
Only other course of action I can think of is to take the head off and see what condition the water jacket is in. A new HG will eliminate any problems with the coolant holes and the possibility of the problem being the HG itself, which I know you don't suspect for valid reasons.
Everything external to the engine itself has been eliminated now.
Kevin