I was fighting GHA and turf algae for months in my biocube and couldn't get it to go away until:
1. Stopped the coral feeding regimen with roids, frenzy and chili, will start again in smaller doses later. I was following the directions on the bottles for quantities to feed once per week and have been for one year.
2. Feeding schedule for fish reduced to every other day. was feeding 5 fish, 8 small hermits, trochus snails large, cleaner shrimp, two pepermint shrimp, and overstocked LPS and softies 1/2 small cube of mysis per day. They ate it all quickly so wasn't really worried until GHA and turf grew.
3. Turned LED light intensity (steve's led) down from 75% to 50% for a week
4. Did 3 back to back 20% water changes using red sea reef pro
5. changed out chemipure blue and added phosguard to filter tray.
6. dumped in 2000 cope-pods, added 2 mini emerald crabs and 4 small trochus snails.
Not sure what did it, but I suspect light intensity and overfeeding was my culpret? And that the chemipure, phosguard and water changes helped shock the algae out. I maintained undetectable Nitrate, traces of phosphate, undetectable ammonia, KDH = 5 to 8.5, Calcium 450. Never tested Mg. API test kit and Hanna for Ca, KH.
Its was like a miracle. No algae in display at all in any hole or crack on any rock, all corals are still very happy, fish still happy. And me, extremely relieved and happy with the results, not even a single blade or spot of algae. Oddly enough, GHA is growing on my overflow on the back portion outside of my display and in the filter area before the small in-tank refugium that is full of chaeto. I'm OK with that so far as it hasn't migrated out and is easier to remove there. . I am a little more careful with feeding but now do 1 cube every other day, roids, frenzy, and chili once per week. Its been 2 months now and no sign of algae in my display.
I am not suggesting you follow this recipe, but only supplying information on what worked fabulously for me. From my limited experience, I might suggest that your tank is still cycling or never completed cycling and with husbandry it will go away?
Good luck to you.