Experiment 1
Summary conclusion: In order to find out if air will stay attached aft of a wheel with a pizza pan hubcap, one first has to keep the pizza pan hubcap attached.
Just to shorten the discussion, I don't need to hear that I didn't put enough velcro on. My experience is that you can tell if velcro will hold without using very much. If I felt that it had a good grip I would have definitely used more, but the problem is that I only have the edge of the pan in contact with the wheel, and 1/8 inch of contact surface is not enough even if I had covered the entire edge with velcro.
I had a feeling it wouldn't work, but it looked good so I took some pix and went for a short drive. Very short. The cap fell off in about a block, and was run over by the rear wheel.
So anyway I have a cap that is ruined as far as an aesthetically pleasing final result, so it will bear the brunt of further experimentation as far as what's needed for attachment. I won't mind drilling holes in it to see what will keep it attached before I mess with the other 3 wheels.
I'm not going to glue it on.
Double sided tape, I think, is going to have the same problem as the velcro in not having enough surface area to be effective.
I don't really want to drill holes in the center area because, though this may work well, I don't think it's as aesthetically pleasing as the pan is hole-free.
I was thinking of the previously mentioned contraptionery in order to have something that could be easily removed without tools, but still stay in place while on the road. I might still experiment with that, but for now it's deciding if I want to zip tie it in place and cut the ties every time I want to check air pressure, or drill a hole and add an extension to the valve, as was suggested, and cut the ties only for rotation or repair.
Thanks for the suggestions, and for following along.