An observation or two that may help at least in understanding if not solving. First,
@Essjay explained the two different scales used, one by the hobby and the other by water authorities, and how to convert. So go with your API test for both tank and tap (inconsistency will occur otherwise) and just be aware of the different values for tap water. Shake the Regent #2 for a good two minutes, including some thumping, and there is no reason to doubt the results.
Second issue concerns plants. Aquatic plants, growing submersed or floating, will keep nitrates
that occur within the biological system low. This is because most aquatic plants take up ammonia/ammonium as their nitrogen, and this means with sufficient plants that are fast growing (floating plants are ideal here) the ammonia produced by fish will largely be taken up by these plants. Nitrite does not result as it would if the bacteria/archaea are using the ammonia/ammonium, and thus nitrate is not produced at the next stage. Some ammonia will get taken up by the nitrifiers but very minimal with sufficient plants.
However, this is not the case with nitrate occurring in the source water. Aquatic plants will not take upnitrate unless they are forced to, which means they have insufficient ammonia/ammonium in balance with the other nutrients and light. Aquatic plant uptake of nitrate is more prevalent in heavily-planted tanks using what we term a high-tech method, with brighter light and more frequent dosing of all nutrients including diffused CO2. For those of us with low-tech or natural planted tanks, there will almost always be sufficient ammonia/ammonium for the needs of the plants. The can and do (if available) take up more than they actually need, which is why good floating plants are often referred to as "ammonia sinks." Quite a benefit.
Nitrates occurring from the biological system are thus much easier to eliminate (or prevent more accurately). Those occurring in the source water should be dealt with before they enter the aquarium, depending upon the level. One of our members
@AbbeysDad has dealt with this issue for many years and has some good information. [Lost my bookmarks recently, but he will see this thread and post I'm sure.]
You want nitrate as low as possible as they do impact fish, slowly but significantly for some species. Water changes help maintain stability, and the nitrate should always be the same from change to change.