I also like the ECT sensor but also for future readers, leaking fuel injectors internally into the cylinders after you turn off the engine will cause this same problem. If you can attach a fuel pressure gauge and monitor fuel pressure when you turn off the engine, I think it will drop kind of fast, on a good car it should last for a long time. For a bad ECT sensor, the computer will try to deliver too much fuel thinking the engine is cold, the temp gauge on the dash and the temp to the computer are different sensors so the dash gauge will probably read correctly all the time. Relays can be an issue but just swap same style relays around to test for that.
Trying to start with the gas pedal all the way to the floor is called Clear Flood Mode, but not all cars have this strategy built into the computer but it still works for flooded cars.