I would add that organic carbon dosing (vinegar, vodka, bio-pellets) works pretty well for managing nutrient levels, but it isn't so good for bringing them down. In other words, vinegar dosing works very well to keep already low nitrate low, but it's not as effective or as easy to administer in situations where you are trying to bring a high level down.
Also, I have seen a few mentions of needing to do many small water changes to bring a high nitrate level down. In reality you can typically do quite large water changes without major adverse affects, assuming that the important parameters (Sg, temp, Ca, alk) of the new water are closely matched to the existing tank water. I know this may sound like it would be a major shock to any system, but as long as it's done carefully it's not so bad. If I were dealing with high nitrate as in this situation I would probably do a couple of @ 50% water changes, then work on dialing in a maintenance dose of vinegar to keep the nitrate down once I get it down.