To have it feel and work like a solid floor, you would have to use 3/4 plywood at the very least, and I'd do it in 1-inch. The problem is that now you're getting into something of substantial weight. I do a lot of fiberglass repairs on sailboats, sailboat cabins are of a sandwich-type construction for rigidity and strength, and an idea came to mind. You could use 3/8 plywood and glass it to make it structurally rigid, but half or less than the weight of 1-inch plywood by itself. Make it into two, three, or four pieces, whatever works for storage and transport, and have it where it all pins to leveling blocks, also fiberglassed. The thought is it will never rot. As for as a cover, I'd look into these little tent-like covered portable awnings with the screened sides. This would be something easy to keep swept too. This is something you can do yourself, and I'd be happy to speck materials and do some dimensioned drawings if you'd like.