Thank you guys for the helpful tips. All 4 of my rims came from Murray Park so possibly one this one could be a little different. I will put the spare wheel on and see if that works better. Also I may try a metal stem as that could be a solution but I want to be sure I can find ones that fit correctly. I always loved the road wheels too but not in the budget now. I appreciate all the help.
John
My '67 had all the hi po stuff, 440 super commando, disc brakes, cop tires, cop suspension, all that stuff. Those wheel covers would come off while driving in addition to spinning. My experience with that car and an '80 Mirada led me to believe the root problem was wheel flexing. I solved the '67's problems with a set of mid to late '80's cop car wheels, no more spinning and no more chasing wheel covers down the street. My guess is those were better wheels.
Valve stems, now think of the force it takes to remove or reinstall a wheel cover, consider the forces involved in getting the thing to spin, pretty impressive. Steel valve stems are mounted in two rubber washers for sealing. By using the stem as a stop you're transmitting those forces to the stem. IMHO, that stem is going to deflect to the limit of those rubber washers, mebbe they'll leak, mebbe later or you may get lucky and be fine. I never tried it because I was concerned more about potential valve stem leaks than the hubcap annoyance.
Sorry to be a wet blanket but after 50 years I still don't have a good cheap solution, other than running without them.
FWIW, my '69 has the optional (very heavy) hubcaps, never an issue with that car.