Jake - Perhaps a chemistry discussion might be helpful.
As I'm sure that you already know, nitrate is generated from the bacterial breakdown of ammonia. Ammonia is generated in a healthy reef tank from the respiration of fish (they excrete ammonia from their gills), and from the digestion of food by other critters, such as your nassarius snails. Nitrate can be reduced to nitrogen gas by certain other bacterial species in an anoxic environment. This is the principle behind "denitrator" reactors, and also such things as ceramic bio-blocks and bio-balls.
And, as you've noted, nitrate can also be removed mechanically by water changes and by plant growth that's then harvested. Nitrate can also be removed indirectly by skimming. Phytoplankton and aerobic bacteria use nitrate from the water, and a skimmer or other mechanical filtration device removes the bacteria/phytoplankton, so the net effect is a reduction in nitrate.
Carbon dosing, whether from the addition of vinegar, vodka, or a commercial product like NoPOX, encourages the removal of nitrate (and to a certain extent, phosphate) by encouraging the growth of bacteria in the water column. Those bacteria are then removed mechanically, typically by a skimmer.
Here's the bottom line without an back-and-forth about the "best" way to accomplish nitrate control - all of the above methods work. And every single one of them have drawbacks, so there isn't a "best" way. As just a few examples of the drawbacks - carbon dosing, if not done carefully, can cause a bacterial bloom which will consume the oxygen in the water column and nuke the tank. Refugiums can remove a lot of trace elements from the water column as the macroalgae grows, and it can be difficult to balance the growth of macroalgae so that you don't cause a nutrient "crash". Sulfur denitrator reactors can be finicky to run, and potentially dangerous to the tank inhabitants if more methanol is added to the reactor than the bacterial colony can consume. Water changes have the drawback of being laborious, ineffective if done on small scales and infrequently, and potentially dangerous to the tank inhabitants if done on a large scale (>50%) and the water chemistry and temperature of the change water isn't carefully matched to the tank water. Bio-balls/bio-blocks are known to cause elevated aluminum levels in tank water over time, though it's up for debate about how much aluminum is too much.
Finally, trying to control nitrate production by keeping a squeaky-clean tank and sharply curtailing feeding has the drawback of potentially adversely affecting the inhabitants from nutritional deficiency, as well as creating a lot of extra work.
Bottom line - After reading through this, I would suggest the following in your situation, but you will have to decide for yourself:
1) Get a good nitrate test kit. Despite advice to the contrary, API's nitrate test is infrequently used by experienced aquarists. Salifert, Red Sea, Nyos, etc... will all work well if executed according to the directions.
2) Perform a series of daily 30% changes for several days, with measurement of your tank water's nitrate concentration every day before you do the change.
If the nitrate concentration is slowly going down as you do this, you can be fairly certain that your tank's bacterial load and skimmer are doing their job, you won't have a long-term issue, and the tank will stabilize at some lower level of nitrate concentration. If that's not the case, and the nitrate level is stable or increasing over the period of time that you're changing water daily, then you will need to intervene by adopting more aggressive measures as described above. Personally, I favor carbon dosing, but I also have a chemistry background and have no problem precisely measuring liquids. Others with less chemistry skill and/or have different preferences may choose the refugium and/or bio-block/ball route.
