I finnaly just put them in the washing machine. We have a front loader with a BULKY ITEM setting. After they were washed, I put them back on the foam rubber cores while they were still wet. Then I put them in the sun to dry. Results were very good. The edging looks no worse now than they did before washing. The nap is pick up nicely and they look good. Most, but not all, stains are gone.
The factory owners manual says to spot dry clean only. Spot cleaning wasn't going to help these covers.