There was a hydroponics setup in Motueka ( I think ) that ran an aquaponics trial with techical advice from Dr Wilson Lennard. His PhD is in aquaponics. As far as I can glean, they had an issue with winter time ... guess the fish don't feed so not much nutrient for the plants. I haven't seen any official report on their experiment but it seemed that that aquaponic plants did better than the hydroponic ones. Not sure what fish they had a license to try and grow.
Apparently for fruiting plants like tomatoes, you need to add some potassium. Chelated iron is a lot cheaper than buying Flourish iron. So, interesting to see you managed to grow tomatoes as the plants are heavy feeders.
My aquaponics setup has been a fizzer so far. The lettuce were attacked by aphids and I didn't notice until too late. Also lack of sunlight so even though roots were over a foot long in the DWC, the plant was just an inch tall and going spindly. My zucchini were also attacked by aphids. Nitrate levels were also unmeasurable and I think this is because I have way too much duckweed present. And also I have far fewer goldfish with only 2 10cm fish, and the remaining 8 being babies in my bathtub.
It was mentioned above that trout would not survive. How about perch? I believe Zealandia has perch in their waters as well as trout and natives.
Dr Lennard doesn't recommend worms. They just create worm casts which is another form of solid in the grow bed. Worms don't break down fish solids anyway, they just consume the bacteria/fungi. Murray Hallam is quite keen on worms .. but we just don't have any comparative data.