We use air decks on top of rib decks, mainly so sit on for long cruises instead of seating on tubes. Have tried all sort of cleaners, no one gentle enough on air deck fabric. What works pretty well and with minimum scrubbing effort is acrylic thinner (AT) sounds cracy, but works.
Make a big cotton pad apply a generous amount of AT and gently rub against fabric, roll the cotton as to rub with clean pad area. When cotton has been completely rolled and there's no left clean area to keep rubbing, make a new one and so forth. If not dirty area of cotton pad will transfer cleaned dirt back to floor fabric.
AT cleans fast and evaporates fast too, if with fear using AC, try it as described on a small fabric portion. The worst you can do is hard scrubbing on top air deck fabric, better is rubbing with a product that removes hard stains, dirt stuck faster.