Adding a refugium to your tank is an excellent idea for more reasons than one. It will help remove nitrates and phosphates. I recommend a refugium highly. But for quickness, the water changes would be the way to go here.
--with most test kits, you have to mix it with salt to the correct SG
before it will register on the test kit. EDIT (this last section is so you can test your distilled water for nitrates).