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I have the same problem with a QJet. I have heard that the fuel pump has a check valve that is supposed to keep the gas from gravity feeding back to tank level, but cannot verify with certainty. Hard to believe that heat can evaporate it back into the feed line, but it might Perhaps someone here can comment? If it doesn't have one I might consider installing one to check my theory.
You probably thought of it already. However, did you check your fuel filters? You may not be getting enough fuel if clogged or if there is floating debris in the line it could occasionally clog the flow. You may want to check your fuel pressure as well where your line goes to the carb.
Kinda sounds like not enough high idle. Maybe set the choke idle screw for a little more RPM. I have a 1406 on a 305 and I just tap the gas pedal halfway to floor once, let off, and crank it over. Always fires instantly and stays running. My cold idle screw is set to somewhere around 2,000rpm but that isnt needed for long. I let it idle high for 10-15 seconds, maybe more if very cold outside, then tap the throttle and it comes off the choke idle circuit.