We have the same chairs in the rear of our trailer. Have the same problem, moving them around. I turned one over the other day and noticed that on mine the round metal ring has 8 small rubber bumpers attached. These rubber bumpers, or whatever they are called, seem to dig into the carpet. I might try to remove 4 of them and see if this helps the problem. Not sure what the purpose of the 8 rubber bumpers are.
Don