Never actually seen it in operation, but I always thought trampoline bed material would be perfect; it's UV resistant, tougher than my banker, and not really expensive; plus it's relatively easy to work with.
It will let water drain through, but provide some solid support.
Trampoline Fabric: Trampoline Fabric Manufacturers, Suppliers, Exporters
This stuff comes in colors and is either 13' or 14' wide; you have to order 3 yards minimum, but for less than $60 you could fashion a floor that I think would be the thing! In case you are concerned the stuff might tear easily or not be up to the task, you could probably double it up and be almost bullet proof.
If I had a cat I'd be looking to try it.