So now we know it is a fuel delivery problem. Fuel is getting to the rails but not through the injectors. It’s a good idea to check the regulator but I’m thinking electrical problem. Heat can effect electronics. I don’t know the schematics for this specific vehicle, but if you can find them you can test for proper voltage to the injectors. A mood light would be very helpful in this case. There is power supplied to each injector, then the ECM grounds that circuit to activate the injector. I’m guessing that whatever sourses the power to the injectors or supplies the ground is fairing when hot. With a stethoscope listen to the injectors while cranking during fault mode. You should hear them clicking as you crank. If you don’t, then follow the circuit that supplies power to the injectors. Then follow the circuit that supplies the signal to the injectors. You may find a bad wire or connector at these points. Pay special attention to the connector at the ECM.