Believe me I know Green Hair Algae STRUGGLE, so when ever I see post about it I pop over.
If you tank is only two month old, then I would say your rocks are leaching out nutrients and phosphates and thus the Green Hair Algae on the rocks.
And while that GHA grows your test kit for Phosphate at least won't read correct. The Algae growing is using up the Phosphates.
If ALAGE is not Insanely out of Control, just keep pruning it. It SHOULD eventually slow down as it uses up whatever is feeding it. (unless you are over feeding your tank)
If Getting bad....and your setup allows you to take out the rocks, then take them out and scrub them of the Algae and rinse off with Salt water and put back.
Don't put back the water you used for rinsing in your Tank.
I wouldn't use any chemical since that could just give you other problems that could be worse.
I never tried NOPOX (bio/carbon source), which I understand can work on Nitrate and Phosphate reduction, but from what I research you need to be very regular and use a good skimmer to export the breakdown of Nitrate and Phosphates into a BioMass. Also your system will get hooked on it, so you'll have to ramp down to get off. (from what I read on peoples experiences)
Your Goal is to EXPORT whatever is in your setup that is Feeding the Algae, which mean either getting nutrients out of rocks (leaching), or feeding less Nutrient IMPORT.
As far as Clean up crew CONTROL, I pretty well tested every kind of creature on GHA in a test tank. Watching with a Time Lapse recording WEB CAM.
Seahares are the best, but they will die quickly once the Algae is gone. I heard that sometime Fish Store will rent a Sea Hare and once it polishes off your tank, you return it.
Next best are Cowrie Snails but only reef safe ones.
And then I would say Emerald Crabs are pretty good for fine Algae plucking work.
Everything else I tried (most snails) really don't eat GHA unless it's very short and fine on rocks.
Also whatever eats your Phosphate made algae will Poo out the Phosphates (pretty sure) so better to pluck and remove the algae, or scrub rocks.
So here is why I know Green Hair Algae (from a few years ago in 65 tank that was about 1 year old, and I over fed the Corals
When it got this bad, the only solution was removing all rocks and scrubbing them down.
I read this and it makes sense. Your rocks will soak up nutrients, nitrates, phosphates in a young tank. Kind of keeping things under control in the water. Then once they can't absorb anymore, the Algae will start growing. Algae will reduce your N&P in your water, and when it's low the rocks will start releasing the N&P which fuels the Algae.
I think that is what happened to me, since for a Long Time my Phosphate was 0.00, and especially when the Algae was Growing. And Algae won't grow with no Phosphates.
Oh...and Last but not Least....If you have control of you lighting
REMOVE any RED LIGHT SOURCE since Algae Loves Red Light
(one reason people run the Algae Scrubbers on RED LEDS), and an Algae scrubber is another Option (Chemi Free Nitrate and Phosphate reduction/EXPORT).