Grey water wicking bed systems and troubleshooting
Some things which may help your conceptualization.
From experience using a grey water wicking bed as a filter and water cleaner
TRANSPIRATION AND VEGETATION
I found that once the vegetation gets going, there may be very little coming out at the end of the system as most of the water transpires through the leaves. Cannas were especially effective in this regard.
CANNAS AND WATER CLEANING
I like cannas as they have a great reputation for cleaning water (I cite some papers in my book)and they have edible roots, but they are invasive.
Invasive plants have been one of my biggest maintenance issues in the grow beds. The cannas tend to stay confined in the bags I use which can be removed one at a time and replanted. Its heavy work replanting but all the soil is root bound and wet so it keeps shape. However, the mint was very hard to remove its roots go through everything, tying the bags together in an immovable network.
CHEMICAL PROBLEMS pH
Based on your filter materials you may have ongoing pH problems. Mine were caused by the use of carpet under felt. The bed still has a high pH after 2 years. If possible use good soil and make sure the stone in the filter, if you use it, is pH neutral.
SODIUM PROBLEMS (FROM SOAP)
I used to use KOH based soap I made myself, as there is no sodium in it and K is part of the fertility trio of macro nutrients. Supplemented with urine I thought my plants would have all they needed and thrive. But with time I've reverted to commercial washing liquid which is high in sodium. I notice that the leaf vegetables are not thriving. Sodium is a thing to watch for, especially if you are outputting from the wicking bed into the garden, as after a decade it apparently permanently salts up the soil, and you don't want that level of fertility dysfunction in a food garden.
The system is very low maintenance. In two years I've done a bit of transplanting and cutting back. With more intensive management it may be very much more productive as a food garden rather than merely as a bio filter.
I certainly wanted my wicking bed for growing copious green vegetables but this is not happening. My successes have been Taro, sorghum, sunflowers, various other grasses which the animals love. They jump on the bed to eat wheat grass for instance. In the beginning the snails were merciless with green leafy vegetables. There were too many places for them to hide between the grow bags, and in the dense foliage. Perhaps you can construct your beds to prevent snail access. I have not found very much information online about what foods excel in this type of setup in an urban garden. The contexts in which grey water systems occur are usually different, large scale, public works and so on. Choosing plants is all a big experiment and we are pioneers in the urban garden. Our city regulations suggest that kitchen water should never be used for the garden because of the fat and chemicals....well, you can change what you put down the pipe, and pass the high nutrient effluent through a worm bin, so that myth is now officially busted. Its a start.
The worm bin at the receiving end of the kitchen water filter removes large particles and excess nutrients and the worms love it. Its been a resounding success. I remove the vermicast and change the bedding material about once every 6 months or it gets so fine and sticky that it clogs the drainage holes. When water doesn't pass through easily it leads to a cascade of problems.
Well that is all for now
I'm excited to hear from you and so happy about what you are doing.