A good way to knock that nitrate down is to schedule some rather large WC's with water as close to your current parameters as possible (temperature, pH, Salinity, Alk)
When I had my 75g, I used a brute trash can on casters that I mixed my new SW in and wheeled it to the tank. Used a pump to get 90% into the tank before having to lift the bucket up for the last 10% (this was the worst, but still easy-ish, part).
My recommendation would be to do 30-50% WC, wait a week, test, do another a 30-50%, rinse and repeat until you get to where you want to be.
@Randy Holmes-Farley has a very good write-up on the effects of water changes with the various methods on contaminants like nitrate as well as frequency effects. At the end of the day it's a dilution problem while the tank is generating the nitrate as well.