Hi All
This is going to sound stupid but it’s true, I had a fault on a car a few years ago that took forever to find, very similar car died when hot started when cooled down.
It turned out to be a porous heater hose, when warmed up it fired a very fine jet of water onto the electronic ignition module causing it to short, once the water pressure dropped the jet of water stopped and the residual heat from the engine dried out the ignition and the car started again.
The jet was almost invisible the only way I found it was when I was poking around the water hit my hand. It wasn’t even enough to drop the water level noticeable.
Anyway that’s the story might be worth a very careful look at the hoses when the engine is hot, maybe around the ecu connections or anywhere the hoses are near the electrics.
Good luck