I filled the gas tank this morning. No overspill! First I set the pump nozzle so that it rested in the fill tube but the pump cut out after a few mL. So I centered the nozzle with the fill tube and pressed that gas vapor/splash barrier up tight against the opening and, voila! No overspill, no pump cutting out... so I guess I can't be lazy anymore while the gas is pumping.

I'm going to continue to pump this way and if I run into any additional problems with the pump, I'll update this thread.