That is exactly what I do when the engine is cold except that I turn the pump on and monitor fuel flow, not pressure, to get 3 GPH and then pump off. With a cold engine that technique works great.
But in the situation I described with a hot engine after refueling, doing that same thing results in exactly zero fuel pressure and zero fuel flow unless I wait for about 20 minutes. I do not normally prime a hot engine after a short time on the ground but in this case I tried that just to find out what is going on. Everything points to the Andair trying to pump air, not fuel, from its inlet port, which it is not designed to do.
Again, this is new. I did not experience it in the past.