Greenhouse waste water filter

I just finished the basic structure of my greenhouse. It frames the south facing kitchen window, so I want to use the opportunity to experiment with gray water.

The current plan is three layers, each 9-12 inches deep. First stage filtering will be something that creates biomass and roots but not edible (currently using hens and chicks) since it will have wastewater poured over it on a regular basis. Water will filter down through roots, sand and charcoal, draining out the bottom.

2nd stage would be something aquatic or semi aquatic. Rice? That depends on how much water it ends up getting. Currently looks like a LOT. Water on this level would probably come in from underneath and drain through an overflow pipe at the expected water level.

3rd stage would be culinary herbs or some such, but I'm not concerned about that one yet. From there, hopefully drip line to water the greenhouse. Maybe switch 2 and 3?

I would be perfectly happy if I could let the plants do all the filtering, but I know that's probably impractical in such a small space.

Any ideas or suggestions?

Not having tried it, my thoughts are that you might get some benefit from running your graywater through wood chips first. If they were myceliated you could get some good filtration. But I don't know if they could handle being that wet.
Second, and I think you were headed that way, I wouldn't grow anything that had the food part of the plants in contact with the water.