How else to do battle with hair algae

[Pescador]

My old 125 looked just like your tank and I was just about ready to throw in the towel.
I don't know what the solution was for sure but I put in three diadema urchins, a new skimmer, and changed to Tropic Marin salt. It cleaned up pretty fast after that.
I still think it was switching salt but that's pretty hard to prove. It's never come back anyway.
Good luck and hang in there.