I'm a fan of my salifert nitrate test kit, and i really did not like my API test. Even if the APIs are accurate (which i never found them to be) they're a pain to use and not shaking the heck out of the test vile for the full time can throw the results off. It's worth the extra $10 for just an easier test, let alone accuracy.
You could also look into a more powerful fuge light? I uae one of these on my QT tank and it keeps nitrates pretty close to zero:
http://www.amazon.com/Finnex-External-Refugium-Breeder-Hang/dp/B008CGWKKM. Granted my stocklist on my QT is nothing compared to what you have going.
What are you using for your filter and how often do you clean/change the pads? The longer pads sit in there, the more poop breaks down and eventually turns into nitrates. I'd try changing them out every 2-3 days or cleaning the foam block.
Do you blow off your rocks? I use a turkey baster from time to time on mine and it's surprising how much stuff i find resting on them. Give that a whirl once a week and see what happens to your nitrates.
What sort of flow pattern do you have? Do you have dead spots? Ever since i put two MJ1200s on the top part of my tank blowing across the top to create sort of a poor man's Gyre effect, my dead spots have basically completely gone away and the tank is much cleaner (and i notice my filter pads are much dirtier).
Vodka/Vinegar dosing are not bad options either, from what I hear, but there are bunch of different ways to achieve the same thing. If you go that route, a $70 BRS dosing pump could automate this except for filling up the container every so often.
When i first set my tank up, i had high nitrate issues as well. I found i hadn't tuned the skimmer properly and it wasn't working to it's full effect. Correcting this made a massive difference.