Howdy- cool experiment.

Just to have mentioned it, I'm not aware of a pathway to eliminate sodium build up in a dead-end system ( not closed, as you're feeding constitutes a system input). Yer pulling very small amounts of NaCl out as plant compounds, but I suspect that you'll have long-term accumulation issues. Yer looking for NaCl in ppm concentrations, but the feed yer adding contains NaCl at part-per-thousand levels. ( Trust me on this- there's no commercial feed available in the world that doesn't have problematic salt levels for this purpose. Pond based aquaculture actually depends on a considerable amount of flow through to keep the envionment sub-toxic.)

I'm also thinking that yer looking @ P defs in flower and Fe problems cross the board- Fe almost unavailable @ pH which will allow for un-stressed fish. Too much stress and you lose that part of the cycle- Fish don't eat.

The turtle's a neat twist, and might actually be enough biomass to get this to work, but I'd watch out for big swings in N level- a single turtle prob defecates/urinates more than the #/weight of fish that the tank could support, but it's in big spikes instead of a slow averaged release. I'd be worried about fungal infections (of the turtle) if you let the tank stay dirty enough to support rapid plant growth.

Have a look @ open cell foam as a filter media- shitload more surface area than rocks. Be nice to get full conversion on one pass thru the filter. Yer filter'll be happier if you can set up some kind of rain box/ spraybar arrangement, or otherwise aerate immediately pre-filter.

Lemme know if I can help with this- I've actually done a bit of it.