Certainly no expert on anything, but I have tinkered with engines for many years.
I think I would try a mechanical temp gauge to see if coolant is actually heating up that fast. Sometimes electrical gauges go screwy.
I also think there is a test kit you can get at NAPA or other large auto stores to test coolant for combustion gasses. Using such a test would be a whole lot easier than removing the heads to test for bad head gaskets. If there is no evidence of combustion gasses in the coolant, I would bet that the head gaskets are OK.
It has been a long time since I touched a Chevy big block and I don"t remember if they have problems with air becoming trapped in the block. Some engines have a plug or plugs that you need to remove to get all the air out after you disturb the cooling system.
I also would wonder if somehow the LP carb was leaning out the air/fuel mixture which would make the engine run hot. No experience with LP systems.
Is there a computer involved? Or is it a simple electric shutdown switch if the temp reading gets too hot? Checking the wiring is a good idea, but breaks or partial breaks are not always apparent. Oil OK? I know that oil seems to last forever in an LP engine.
As someone else posted, I have had an impeller come loose on a water pump shaft, but once it came loose, I had no coolant flow, not intermittent heat readings. It got hot within a mile or so. I really doubt that is your problem.
So I would suggest verifying that the engine is REALLY getting overly hot and if it is I would check for combustion gasses in the coolant. Hope you can find the problem and it isn"t too expensive or hard to fix. Good luck!