Very low salt solution could work, EG Sea-90 at hydroponic rates (something like 1tsp dry matter/gallon water). Nothing lives in completely pure water, ya dig?
I think you may also want to peruse reef or planted systems that include a sump and/or refugium. A refugium would be where you would house your bio-filter most easily. Being as it's only a biological filter bed, you wouldn't need to light it as many refugia that are utilizing macroalgaes do, because the purpose of the macros is to utilize excess nutrient load. There are indeed saltwater vascular plants--mangroves--and there are indeed people rockin' them. These areas are generally fishery nurseries, where you'll see larval and older forms, as well as lots of sponges, hydra, anemones, bivalves, filter-feeders mainly.
In a freshwater environment, that role can be played by many plants, including many popular houseplants such as Syngonium. Or, even better, cannabis.
Now, remembering that I only have experience in the aquatic side of things and not marrying aquatics with hydro, I personally would contrive to disturb the biological filter bed as little as possible. That means I personally would not bury the plants or situate them within those beds, I would site them remotely so that only the same water column is passing through the filter bed media and the plants, in whatever order. You see, the plants will also be achieving some filtration in this scenario, and depending on direction of flow, I can see them being able to utilize both NO3 and NH4. Every time you disturb the biological filter bed, you're pressing a reset button, so it's really better to leave it as undisturbed as possible. If it needs cleaning ever, I wouldn't ever do more than 1/3 of the total volume at once, and I say that because I've killed too many fish doing more.
Your biological filter bed can be as simple as a large trash can filled with gravel of graduating sizes and sand, trickling downward and then pumped back through the system. You just need a pump that can do the job, Iwaki and Little Giant are two faves of mine (and the Long Beach Aquarium of the Pacific, probably other public aquariums as well). I would go with external pumps in this scenario.
The standpipe you're describing sounds like how we did the filtration at Petschmo HQ distribution center. Kind of like Durso standpipes, but we really didn't care about the noise. All 700 freshwater tanks and 300 saltwater tanks were tied to the same systems. Did you know that you can walk on a row of aquariums? You can step on an aquarium, too, even as small as 10gals, you've just got to do it a certain way.
So, what you'll really need in this setup is an automatic top-off rigged up, otherwise you could end up killing some equipment due to evaporation. I figure given how low you've been reporting your local RH to be that you could lose a LOT of water just to evaporation, and an auto top-off would save your skin there in a big, big way.
Oh my God, I just thought about our ENTIRE BASEMENT SET UP AS A FISHROOM!!! Just the thought gets me giddy, can you believe that?
Giving it some thought, and I'd like stutter to confirm or deny whether or not this is a workable solution, I would place the plants between the fish and the bio-filter, so that the plants can take up as much of the available nutrients as possible BEFORE they're processed by the bacteria.
So.... Fish --> Plants --> Filtration --> Fish
Make sense?