Jack your car up and put a bathroom scale under a wheel. Deflate the tire
and then lower it onto the bathroom scale enough to make the sides bulge out
the same amount as when it's holding up the car. That's how much you have
to add to the pressure x area product. My guess is it's going to be a very
small correction.

To measure the footprint, I would dust a piece of dark colored paper with
flour, and slip it under the jacked-up wheel. Lower it and raise it, and
then take the paper inside to the desk where you keep your planimeter.

Or you could cut out the footprint with scissors and weight it on a delicate
scale.