According to
this thread, Yes, A remote DSB can remove nitrates.
It's been tried and tested by many people.
The concept makes sense since you're relying on the metabolic action of cryptic, anaerobic, chemotrophs to facilitate nitrate removal.
As detailed, the process seems to have some down sides, but i have some ideas for fixin' those problems. One of my favourite subjects (i'm kinda weird this way) is methanogenisis.
People who run methane generators, especially for prolonged periods of time, have similar problems to the ones described. I wonder if the solution might be the same.
In methane generators, Carbohydrate and Nitrate need to be kept in a specific balance. I think that the problems described in the remote DSB thread corespond to carohydrate deficiencies in the chemotroph's environment. This accounts for the variability in the success with the method, as well as for the cycling that seems to occur. People With a low TDS would see less results since the bacteria wouldn't have an adequate carbon receptor to facilitate the removal of nitrate from the environment. Chemotrophs are simply another form of hetereotroph, and many are capable of predating other microorganisms, or even cannabalization.
Also as a final note on the Remote DSB, i see alot of people wondering why a DSB would need to be unlit and not very well oxygenated for the method to work. From readings that i've done on anaerobic detrivores that live in the soil, they're one of the few organisms that can fix atmospheric nitrogen into nitrates (the organisms really do need nitrate that badly.). Allowing light and Atmospheric air to reach the substrate is only going to facilitate this an environment where the opposite of the desired effect occurs.
In regard to the Deep Calcium reactor....
It depends on how you ran it. Since you mentioned Dosing Carbon dioxide, i remember briefly skimming a thread a few months back that talked about Calcium acetate. It might be something worth looking into. If you're in the US you have to make it though, but since all you need to make it is powdered Lime and cold White Vinegar, it shouldn't be too much of a problem. I do have to warn ya though, this is effective carbon dosing, since acetate is a simple organic molecule, and it could result in a bacterial bloom.