How do you know its truly zero if the hair algae is consuming it? Yes I agree hair algae is far more resilient but the real reefs have almost zero phos and Nitrate. Yes they circulate a lot of water that only has tiny amounts but at the same time they have no hair algae.
Anyway I am pretty much out on this one. I have seen 17 years of these kinds of posts and the actions taken are almost always to add some kind of chemical to the water.
Well i did go for several months without adding any sort of nutrient to the tank and the test registered zero for both phosphate and nitrate for several months. No fish in the tank. Hair algae stopped growing during this time but didn't die. Coral all began to bleach and stopped growing completely. Lesson learned here is that you cant starve hair algae to death and expect to keep coral living. During this period the tank got hit with dinos and still has hair algae... I believe it all points to the tank being truly nutrient limited: dying corals, no growing algae, no fish, no addition of any nutrient source for months, Dinos popping up...