I was in the same situation about 2 months ago. Although my setup is much smaller: 55 gal tank and a wet/dry filter converted into a sump/refugium. I have 3-4 inches of sand, a small amount live rock, and a big handful of chaeto in the fuge. My nitrates were around 15-20 ppm and would stay there even after 20% water changes. I was feeding my fish daily with powerheads running. After doing some reading on how to deal with nitrates, I decided to turn my powerheads off during feeding so the food would not blow around the tank, and to feed every other day. Doing that along with additional water changes brought the nitrates down to about 5 ppm. I was at a local fish store and asked the owner what macro algae were good at removing nitrates. He said caulerpa works really well and recommended it. So I bought a handful of that and added it in my fuge. After a week and another water change, my nitrates were unreadable on my API test kit and have been so for over a month now.
One thing about caulerpa you should know before buying any. It reproduces asexually. When it does this, it releases spores into the water that will cloud the water and lower the oxygen levels. This can be deadly to your fish. For this reason some people avoid using it. I have read that lighting it 24 hours per day may prevent it from trying to reproduce. I don't know if this works or not, but I am doing this on mine.