I've used a upholstery cleaner from a rental store to clean cushions and mattress covers a couple of times with good luck. It's easier than stripping the covers off the foam cushions/mattresses. I don't know if it will work where there's a "dry clean only" warning label, but my guess would be that with the covers still on their cushions the covers probably wouldn't shrink -- these machines spray a cleaning solution onto the cushion fabric and then immediately vacuum it off. The process leaves the cushions slightly damp, not wet. In my experience this type of cleaning won't remove heavy grease marks or stains, but will clean surface dirt and suntan lotion residue.
I've used the 3M Scotchgard foam cleaners for years but it doesn't remove any stains. I can't be certain the covers are clean till I send to the cleaners. Hopefully that won't send me to the cleaners as well !!