tire pressure

a shorter tire will leave the beam sooner. a taller (aired up) tire lwill stay in the beam longer.

The statement needs a little clarification. A "tall tire" isn't the same as an "aired-up tire".

A measured taller diameter tire will stay in the beams longer than a measured shorter diameter tire because of the overall size. But once you start airing up any tire, while it will become taller, the actual footprint will decrease because the measurement across the bottom, at the height of the beam will decrease. So it will act like a slightly shorter tire when inflated more. i.e.: At the same height off the ground, measure the bottom of a flat tire vs one that's aired up to pretty much being round.