if you have an engine at peak EGT and you make it richer, which by your example means it will get cooler, why then does it get hotter (CHT) when the EGT is falling? And once past about 50 or so dF CHT will drop again.
The total energy released reduces as you produce CO instead of CO2. Total energy is divided between turning the prop (power), heating the engine (CHT) and out the exhaust (EGT).
CHT can increase while total energy decreases if there is a reduction somewhere else e.g. power or EGT. As you said, keep adding fuel and CHT drops too. No-one said that all temperatures had to drop in synchronization.
You can't create or destroy energy. The peak pressure point is a furphy - it cannot change the amount of energy you have, just where it ends up. If the peak pressure is later and CHT goes down, it means more energy goes out the exhaust or (possibly) turning the prop instead of heating the engine.
Adding fuel
when you are limited by O2 (rich) means that the amount of energy released is reduced. Listing other factors that also result in a cooler engine doesn't change this fact. I'm not arguing with those factors - just the proposition that fuel doesn't cool. It does, unless you are LOP.
Lean mixtures causing detonation is something that has been documented for a long time in many different engine types. Maybe George Braly has shown that Continentals/Lycomings have enough detonation margin to run LOP without detonation. (You might however ask the question whether that margin belongs to the engineer or is the end user's to use.) That doesn't mean that every engine has the same margins.
I somehow doubt that he has done extensive testing of Jabiru engines and their detonation margins. Without that testing, suggesting that Jabiru engines would be more reliable if they ran leaner is dangerous guesswork.
The thing that worries me about this whole LOP thing is the number of pilots who think that every engine can be run LOP without danger, and that LOP is the answer to all engine problems. There is too much evidence to the contrary for me to believe that.