I am sorry to read this. Hair algae can be a bitch, especially when you arent able to find the source. Nitrates are rarely the issue in the case of hair algae, although it is indicative of other issues. Typically hair algae is caused by phosphates and lighting. It can be an issue where you po4 is reading near nothing because the algae is eating it all and not allowing it the chance to convert the nitrates. You need po4 to get rid of nitrates.
My opinion...the rock age is a dead give away. It probably reached its breaking point, especially if it was from a tap water or neglected tank. Basically you are hitting 'old tank syndrome'. It is where you can not fix what ever is happening to the tank and it seems impossible to get ahead of the issue. Many people never learn what causes the tank to crash even. IMHO and it is just assumptions as I have no clinical information to substantiate my idea, is that older tanks rock has been saturated with things in tap water, metals and other contaminants over the years. Eventually they can not absorb anything more and end up leaching out the build up back into the tank. At that point their is no fixing it. Just waiting and hoping. As RO/DI is gaining traction and salt mixes are getting better you are hearing less and less about old tank syndrome. It could be a coincidence, or it could have some traction to the idea. You could have a ICP test done, that will test for many trace elements and metals that could be the root cause.
I personally would look at starting over. Sell the rock to a FOWLR set up where someone can use chemicals to control what every issue or use it in a garden. It is going to take a shit ton of work to strip that rock of what ever is in it.
Of course the other option is to wait it out. It could day weeks, months or even years to get things under control though. It is impossible to tell. Lots of HC GFO, Carbon, water changes, biopellets or other removal media. Replace it often.
I personally just switched to a Zeolite system on my frag set up and ultimately will be for my main system. It basically has you adding something daily, some of which can not be done with a doser. It is a lot of work, but only 4 days in and I am already seeing a difference in the tank. The only other thing I did was add a cheato ball after London Fragfest.