Trust me, I didn't think of it either. I found it by accident.
This was my 87 Diplomat I swapped a 360 into. Anyone that's ever seen the stock exhaust setup on that thing knows how well hidden the flapper is by the pre cat.
I replaced the fan clutch, water pump, belts, thermostat, cleaned the block with old school cooling system cleaner (the two part type).
I even found out that I could put the 87 pickup radiator, with HD cooling, into the Diplomat if I used the truck lower hose.
All of that did diddly and I was dropping the exhaust to check for pluggage when I saw the valve was loose and flopping.
Fixed the flapper and it all went away.
It took months of trying to figure it out.