Thanks for that suggestion. It might work to move just some tires (without wheels), but maybe not secure/stable enough to store four full 20-inch wheel+tire combinations.
I was thinking about something like this is (except with a secure U-shaped handle to make moving easier):
or
The trouble with all the tire/wheel dollies on Amazon is that they are now apparently all made of some kind of plastic. Reviewers complain that they break or otherwise don't hold up.
I am going to try to take a screen shot of one of the professional ones (from F1 racing) the next time I see one being used in a racing paddock.
This appears to be the exact one shown in your picture. In fact it looks like the same picture.
https://www.amazon.com/John-Industries-JDI-TT1-HD-Heavy-Duty-Tire/dp/B07FYNQZXX/