Backyard Aquaponics
A place to discuss aquaponics

I dont see why you cant do it. Get as much grow bed/filter area as you can but dont be over concerned about the 2:1 ratio. You can also put water plants directly into the pool e.g. water lillies, reeds etc which will not only help to remove the nasties but will help cover the water surface from the sun, reduce evaporation, reduce algae buildup, and provide shelter for the fish. Match the fish density with the growbed size and not with the pool size.
If you have a look on yahoo! groups under swimming ponds, and google "swimming ponds" or "natural swimming pools" you'll find a fair bit of info. There was another swimming pool topic on here that I posted some links on. The yahoo group aren't really into growing vegies but rather creating a chemical free swimming pool. But they are quite happy to have fish in the pool along with lots of water plants. The bloke who set up the yahoo group has put his gravel filter on the floor of the swimming pool.
I've tried to convince my wife that we should do the same thing, and have assured her that she could still swim in it but she wont have it ... yet. You're either not married or your wife cant swim. ?

The "natural swimming pools" thing is awesome. Saw it in Organic Gardner once - it's the same "jist" as AP - you set up a ecosystem which keeps the water clean. The one I saw used diverted the run off from the driveway etc to the pool so that it didn't need external water sources (ala naturale!)