Hi Albert,
If your readings of zero nitrates and phosphates are correct, and you still have a cyano problem, then one of these two scenarios might be applicable to you:
1) your tank is in perfect equilibrium, i.e. your cyano is consuming all nitrates that are formed, thus the zero readings.
2) Your tank is too pristine. Cyano is the only thing that can grow in this condition, since it is the only organism that can take nitrogen from dissolved nitrogen gas, and use it for nutrition (almost all other creatures require nitrogen in some complex or organic form, such as nitrates).
(For case 1)
You can attempt to do a one-time cleaning of your rocks to remove the cyano (pls do this underwater, while keeping the rocks in another seawater container, you don't want the nitrifying/denitrifying bacteria in your rocks to die out.) A toothbrush should do fine. Return the cleaned rocks back to the tank, taking care not to bring back any cyano particles. If you do get a low non-zero nitrate reading a few days after this, then you indeed have case 1. In which case, you can get some macroalgae (preferably Chaetomorpha) to mop up the nitrates. Or failing in that, you can leave lights on 24 hours to induce green hair algae to grow (its easier to control than cyano, and slightly less ugly-looking). Or again failing in that, you get some fish which eat cyano (not too many of them, but I know that an Istigobius ornatus or Istigobius decoratus will do the trick).
(For case 2)
This is the curse of the super-clean aquarium. Public aquaria know about this, and never allow their nitrates to reach zero! Otherwise, they get cyano in the form of brown scum all over their walls and rocks, which is a pain to clean. With zero nitrates and miniscule (almost zero) phosphates, only cyano have the capability to survive, and they will quickly take advantage of that situation. Instead of absorbing nitrates from the water, they begin to source their nitrogen needs from dissolved nitrogen gas (very clever of them, only a few other bacteria can do this trick!). The solution? Believe it or not, reduce your cleanliness! Increase your nitrates to maybe anywhere from 1 to 5 ppm. Don't do water change that often (reduce to every 3-4 weeks?), and don't be obsessive-compulsive in cleaning and husbandry!
Anyway, yours is a nice problem to have. You've gotten the proper lights, you've installed a decent skimmer, and a mini-refugium to boot! (I'd suggest you begin worrying about temperature in the next few months, before next summer arrives). You're ready to take care of soft corals. Whenever you want them, I can pass on some small hardy yet pretty soft coral frags to you. Just give me a week's notice, since I've been very busy of late.
I'm just a PM or SMS away.
Phil