That's a big job- a full disinfection and restart- and it may not solve the problem, it still might come right back.
The substrate will need more than a rinsing, it will have hair algae in it too, like everything else (filter included), and will need a bleach treatment also- which will kill the nitrifying bacteria in your filter. Not only that, its probably also in the intestines of your livestock, which could also reintroduce it.
I don't know if this will help your tank, but IME, hair algae only showed up when Macros were low. Have you tested your Phosphates and nitrates? what about K dosing?
If I were you I would try one more time before I give up. Take out your daily handful, as much as you can. Cut photo period in half, stop dosing micros, test macros and add accordingly to get them up. Give it a week and see what happens. Amano and cherry shrimp will also do a number on the stuff, so if they could survive the other livestock in the tank you should try it. Good luck.