OK, well lets think about this some more. It takes air, fuel, spark & compression to make em run, so what's going missing when it won't start after an hours hot shut down heat soak?????
Seeing as it'll start if you open the throttle a little, it sure sounds like its a fuel delivery problem of some sort.
SO, is the fuel old, such that it might be winter adjusted for a lower vapor pressure???? If so, it could be vapor locking after a hot shut down heat soak.
I've also heard of coilpacks & icm's offering up trouble with a wimpy spark after a heat soak.
Is the battery voltage up to snuff after a hot engine shut down heat soak???? Monitor it while your helper cranks the engine.
I have the code 10 as cyl 1 low on cyl balance test. So does cyl 1 have a compression problem????
Did the problem come about suddenly, after some event, or slowly over time????