unwritten, check that filter for TDS (hopefully you got one with the filter)
what kind of hair algae is it? if its bryopsis you may want to do the Kent tech magnesium nuking as the last resort, or maybe, get an emerald crab if you got rid of yours already (i remember something about him bothering the shrooms?) I think my emerald is the reason i was able to get my bryopsis completely out of my tank. Whenever i get a coral frag with bryopsis growing on it from the seller (too often) i give it to my crab and within the hour the frag is cleaned and returned all ready for its final destination lol. Hard working crabs, these emeralds, i am sorry you had such a mishap with yours
as for blackout, that will probably kill your corals more than the algae. if there's any trace of a nutrient, i be the HA will revive despite a blackout .Its such a hardy SOB that its hard to just reduce your nitrate and phosphate and other nutrient addition and actually get rid of it completely.
idk how else to help you man, im sorry