[Zeke]

The tire deflects when on the ground, both out to the sides at the bottom and I suppose a little deformity elsewhere. On the old bias ply design, the overall diameter may change a fraction, I don't know. The air does not compress that much more and therefore the pressure does not go up by an amount that would make airing the tire more difficult. What I do know is that I don't see any racers making sure there tires are on the ground before adjusting pressures. Taking temps, yes.

To fill a tire faster, you need air volume. If you had a 1" opening between your charge vessel and the tire, 2 pounds difference would equalize almost immediately. If you are going to use the valve stem, it is extremely constricted with the valve inserted. That's why tires shops initially air up a tire with the valve out of the stem. They need the volume to air up more quickly and seat the bead.

If you have a large pressure difference between your filler air and the tire, more air is forced by the valve. You can see how this works if you start with a vessel charged to 40 lbs. and use it to air up a tire to 32. As they become closer to being equal, the volume becomes low. Increase the opening and, as I said, the air will move between the 2 faster. Or increase the pressure from the air source.

Having the car on the ground has nothing to do with it in practical form. I'm not saying that scientifically one can't measure the weight of an object by taking pressure differentials laden and unladen, but I am saying one won't notice any difference in the speed in which air is transferred until the volume of air transfer is allowed to increase.

Conclusion: higher air pressure differential and/or higher volume are the only 2 ways to air up a tire faster.