I looked at several used dishes and none of them were circular, but I do not think that they would work unless the section was spherical.
The scratches look bad, but those would only look worse over time. They came that way! Putting a "lunar curve" on the covers might make them more aesthetically appealing--until they get scratched up.
Wouldn't curbs only be able to scratch the edge of the disk?
I just planned on making covers that centered and came to the rim, more or less, sitting on top of any wheel weights. I had thought about trying to find a shallow dish at the restaurant supply outlet.
How about a lid?! A perfectly round dish would require a flat base, which would be fine, but a lid could be perfectly round!
I wanted to go to the store today, but everything depends on paying my rent. It was due the first, when I had drill, with a test the day before, and another test after drill. I tried looking for my checkbook, but of course, as soon as I came home today I saw it.
As for a design on the surface of a flat disk, I thought that would be obvious!