".. do run....when the key is out....if the system is very hot..."

Are you sure of this, CERTAIN sure..??

"...coolant pumps.. will continue to......"

Obviously you're uncertain of "this".

Since it is the METAL engine block that has been, potentially, overheated/overstressed you must be CERTAIN that the radiator cooling fans will run in EV mode as will the coolant pump. I would assume both of these are 12 volt devices and thereby powered from the 12 volt battery which in turn relies on the DC-DC down-converter from the hybrid battery for its own state of charge.

In the conditions related aren't the chances quite LOW that the hydrid battery had a reasonably high level of charge?

"...fairly steep rough road (Jeep trail).." "..involved some steep inclines.."

Seemingly, assuming speed was mostly DEAD SLOW (Jeep trail), there would have not been much opportunity for the use of regenerative braking to keep the hybrid battery charged. "Dead slow" would also imply that the electric motors were in continuous heavy use and with only the ICE "excess" power to use for recharging.

Lots of good reasons for why the FEH/MMH series nor the RX/HL hydrids are NOT qualified, NEVER to be used, for off-road, " Jeep trail", use.

Bottom of the line is that the coolant may have boiled regardless of the operation of the radiator fan and coolant pump.

With HEAVY use of the hybrid battery being highly likely did the system need the A/C to keep them cool. More loading of the ICE and a substantial lowering of the efficiency of the engine cooling system.

Most A/C's will automatically shut off if the engine water jacket temperature is threatening to reach criticality, but maybe not the FEH/MMH since it is used to cool the hybrid battery?