I'm probably talking to a wall here but...
Hair algae feeds off phosphates. You introduce phosphates via food, waste, fish death, etc. Big al's have nutrient (phosphate) rich tanks because they mostly sell fish. You don't just "get" hair algae, it's everywhere in reef tanks. If you don't eliminate the phosphate the sea hare is doing nothing more than a toothbrush would do: stripping off the visible algae. The sea hare will likely die (they often do) and your problem may (likely) return. More phosphate=more algae.
You need a proper phosphate test kit. You need GFO. Phosphates should be less than 3 parts per million.
What comes next if phosphates continue to rise will be slime algae which even sea hares won't eat, and if things get wonky enough, dinoflagellates. Then you get a big, nasty tank crash. Average time for a crash is 3-5 years depending on bio load, but it's more or less inevitable. Constant water changes with 0PPM RO/DI water can help the issue a lot, but not eliminate it, as rock and substrate become phosphate reservoirs (sponges). I really do know what I'm talking about. I run GFO 24/7, have tons of sps, and have recovered a tank that was 90% slime (slime is really really nasty). I mean, for the price of a small reactor, pump and a tub of gfo, it's almost crazy not to get one set up. Or even bio pellets, which I run, but don't think are as necessary as GFO.