You can hang stuff to paint it, but if still leaves a "shadow" where the wire was.
Your wheels do have some pretty bad pitting from rust. Are the wheels anything special, or would it be easier to just get some new wheels?
One advantage of laying the wheels flat is you can more easily get a uniform coat around the wheel. Another possible solution is to thin the DP epoxy (2 parts DPLF, 1 part DP402LF. 1/2 part DT reducer), and spray wet, almost to the point you get "visible flow out indicators"
Some people call "visible flow out indicators" runs.
Painting the wheels can be tricky. It is hard to get paint into the narrow slots between the hub, and the wheel, without getting too much paint on to adjacent areas. the spoked wheel were even more troublesome, because I had to paint the edges of the spokes first, and then the flat more visible areas of the spokes, and finally the rim of the wheel.
Maybe some of the professional painters on this board can do a wheel like that quickly, but I resorted to adjusting the fan width, and paint flow down to a small fan. to do some areas, and opening up the controls on the gun to do other areas.