What this amounts to is that your feeding is adding more nutrients than you’re exporting. Your tank, if you have live rock, even without a protein skimmer, refugium, carbon dosing, algae scrubber, water changes, etc., should be able process some nitrates into nitrogen which should gas off the surface of the tank, so in the absence of those other types of nutrient export, you need to find a balance between importing and exporting nutrients. The more types or the more productive/effective your additional nutrient export methods, the more you can feed/the bigger a bioload you can have. I would recommend a protein skimmer and/or a refugium in addition to the water changes if you want to lower your nitrates and continue feeding the way you are now. If neither are possible on your tank, you could try carbon dosing (though I wouldn’t recommend it, and it would be less effective, if you don’t have a skimmer, if you don’t have a skimmer, but still want to try, I would definitely use an air pump with an air stone to increase oxygenation).
Anyway, all that said, most soft corals and LPS should be just fine with 20ppm nitrates. 40ppm is getting into territory where some LPS would start to be unhappy. Also some soft corals, like Xenia for example, are almost as effective as Chaeto in terms of nutrient export, so depending on the corals you’re adding, you may see nitrates go down slightly. Also, would probably be a good idea if you’re going to start keeping corals to get better testing kits. API is at best going to give you a broad range that your actual values are at, which when you get beyond beginner corals just isn’t adequate.