I believe I have now beaten it (3 months and not a spec to be found) after a brutal struggle - over most of an 8 foot tank
Low/zero nutrients isn't a magic cure because in reality unless your tank is fallow your adding nutrients to the water column and the GHA is first to take it up. If your testing zero, a fun experiment is to manually remove all GHA from the tank, then test the next day - you'll be amazed how much it is pulling out of the water - if only we could harness its strength for good and not evil
I found blackouts useless too. I put a rock with GHA in my sump in total 100% blackout for 2 weeks, then took the cover off and it was still there, weakened but returning to full strength within days under low room light (not even tank lights)
How I beat it (you won't like this) was when I moved house. In the weeks leading up to the move I started taking out the sandbed, 20% of total per week. Then on move day I scrubbed every individual rock under bright light and got out 'most of it' - it can be a turd hiding inside live rock crevices
Set all rock up in the new house (different tank no fish yet) filled with 100% fresh saltwater = zero nutrients. Put a blanket over the tank for a whole week = blackout. Trochus Snails in. Another week later added lights and fish. All equipment vinegar bathed.
The GHA hasn't come back. I blame the sandbed as the nutrient source, old water (didn't do water changes on the old tank, ICP showed all was good but I believe it was old/dirty/organic laid water).
Today I have no sandbed, rocks configured in a better way to allow flow from behind, and use an auto feeder during the week which feeds about 1/2 what I used to feed manually = forces tangs to graze. I run chaeto, GFO and carbon reactors.
I struggle to keep detectable nitrate/phosphate above zero (which has it's own challenges) but creates an environment GHA doesn't like. Worth noting my rocks are mostly covered in Coralline but today the Tank grows coralline not GHA.
My lighting is relatively low (Radion G4's running AB+) - 200 PAR at top of rocks, 130 odd where most of the rock lives (which is why I believe the Coralline is thriving in 'low intensity blue light').
In summary - what worked for me to beat GHA;
* Remove or regularly and thoroughly clean your sandbed
* Scrub / manually removal 100% of GHA - not 90% but 100 then be relentless on stopping it from taking hold again - if you scrub in tank, you have to get it out
* If like me it takes hours to remove weekly and you can't win the war, maybe remove some/lots of rock to a manageable amount (you can add it back later slowly)
* Have 'clean water' as opposed to zero nutrient water (if its yellow or stinks you have an issue)
* Ample CUC - only effective before it grows but effective on keeping rocks clean and ready to grow Coralline
* Hungry fish - so they are constantly pecking/grazing the rocks (don't starve your pets - balance)
* Liberal feeding - fish always look hungry
* Go easy on light intensity at the start until you have good Coralline or Coral coverage on the rocks. Dry rock in the first months shouldn't be blasted with high PAR
* GFO and NoPox (if and only if you have high levels of nutrients - phosphate > .1, nitrate > 20)
* + general good system design for flow and detritus removal, nutrient export