UnCrash
Thanks for popping this into "tips and tricks", hopefully it will help someone.
To start with, let out most of the pressure and break the tire bead so you can start taping the tires off from the bead all the way around. When they are all masked off, toss 10 or so psi in them to keep them nice and round. I was able to lay the wheels on their sides on a few layers of cardboard and just spin them on the axles while I painted. This trick also helps prevent the inevitable first scratch when you mount the tires the first time.