Honda, you are correct that lean operation causes excess heat, not rich operation. And it doesn;t take much. Rich operation only causes carbon. When you use a bellows in a fireplace, it doesn’t get suddenly hotter because you added more fuel, it gets suddenly hotter because you’ve added oxygen. It should be noted that an EGR system cools the combustion temperature by displacing a bit of the oxygen with inert exhaust gas, whose oxygen atoms are already bound up with hydrogen and carbon.
As has already been pointed out, a plugged exhaust can also allow the manifold to go cherry.
Excess spark advance can also cause a cherry exhaust. My guess is that when Bing crossed the wires he introduced this condition. But I’m not seeing preignition in the OP’s description, so I’m inclined not to suggest that.
Regarding the question of which timing condition causes excess heat, it’s advanced timing. Retarded timing causes combustion while the fuel in the cylinder is decompressing, creating less heat than combustion during compression does.
EDIT: I just realized that retarded ignition will send lots of still-burning and unburned fuel into the exhaust, so in essence it WILL heat up the exhaust manifold… and on this engine that may include the cat converter.
Which brings up the added possibility of a valve timing problem…