Many people will do just that, get an urchin to mow down the algae. But it will mow anything in its path, including the coralline. If you have no problem growing coralline algea then go for it. The urchin will eat the coralline and at the same time spread the spores.
I still think it would only be a short term band aid though, sounds like you still have some form of nutrient problem, even if it is only slight. The hair algae is using whatever it can as fast as it may be going into the system.
Have you tried changing the food that you add to the tank, reduced feedings, run a polyfilter, drip kalk to reduce phophates, phosphate sponge, more frequent water changes, are you running carbon 24/7 if so then perhaps you should stop with the carbon and only run it once every couple of weeks. The list goes on and on.
Thomas