The problem with getting a mineral or a polymer that binds nitrate is that there is very little that is chemically special to hold onto.
Nearly all nitrate salts are soluble, unlike many phosphate salts (calcium phosphate, iron phosphate, lanthanum phosphate, etc.).
In the long ago chemistry days, before machines like ICP, one would try to determine what unknowns were by the physical properties they showed. Nitrate stands out as nearly always soluble:
Practically all sodium, potassium, and ammonium salts are soluble.
All chlorides, bromides, and iodides are soluble except those of silver, mercury(I), and lead(II).
All sulfates are soluble except those of strontium, barium, and lead(II), which are insoluble, and those of calcium and silver which are moderately soluble.
All carbonates, sulfites, and phosphates are insoluble except those of sodium, potassium, and ammonium.
All sulfides are insoluble except those of the alkali metals, the alkaline earth metals, and ammonium.
All hydroxides are insoluble except those of the alkali metals. The hydroxides of calcium, strontium, and barium are moderately soluble. Ammonium hydroxide does not exist; ammonium hydroxide is a misnomer for aqueous ammonia, NH3(aq).
In terms of a binding polymer, nitrate sort of acts like a generic negatively charged ion. Since there are many others in seawater (notably chloride and sulfate) at far higher concentrations, you'd need to bind nitrate selectively over these others, and there's just no way to do that easily with an organic polymer.