I've posted this before - so I'll just post the link:
https://www.reef2reef.com/forums/reef-aquarium-discussion/90291-cyanobacteria-problem-nitrate-2.html#post990089
Your nitrates being undetectable may be contributing to your problems with cyano. Its really not that big of issue to have elevated nitrates. You've probably already see this video:
Aquariums - David Saxby's Reef Aquarium (extended version) - YouTube. It's a remarkable tank and at the time this video was made, his system was testing 5ppm nitrate. So a little nitrate isn't going to hurt your tank like everyone thinks.
Cyano dominates, especially in new tanks, because it doesn't need nitrate/ammonia to grow. It get its nitrogen and carbon from the atmospheric gases dissolved in the water - carbon from CO2/carbonate and nitrogen from N2. The only thing it needs is phosphate and there is usually a good source of that from gravel and/or rock (esp dryrock) in the tank.
Actually if you increase your nitrogen (nitrate), you'll increase the ability of other non-nitrogen fixing algaes and bacteria a chance to compete with the cyano. Ideally you want to maintain a ratio greater than 16Nitrogen to 1Phosphate otherwise cyano has the edge.
I have actually found it helps to dose nitrate to a new tank to get it through the cyano phase quicker.