Cyano battle I had experience with. Together with battling the symptom you need to battle the source.
Cyano is particularly difficult in that it reproduces extremely fast, can fix dissolved Nitrogen from the air (Not necessarily Nitrates) and feed from Organics like fire on dry paper. It also thrive in mostly shadow areas were it is most difficult to extract.
As removing Nitrates will do little for Cyano (Although will do wonders for getting rid of other algae) I would be looking to reducing phosphate and specially organics. Unfortunately that is the one thing we can not test for reliably or cheaply.
To address the problem:
a) Revamp your skimmer. Try to increase it's efficiency, set for a little wetter foam and clean it at a minimum twice a week. An oversized skimmer could be your best line of defense.
b) Insure that your light bulbs are replaced regularly, old bulbs shift spectrum to what Cyano loves. Replace them once a year as a minimum.
c) Increase your water flow or direct the flow to areas where water can move too slow or get stagnated around the tank.
d) Reduce your feeding to the minimum necessary using dry foods or frozen foods that have been thawed and washed before feeding.
e) Reduce Organics by the use of Activated Carbon AND Purigen. Wash the carbon well and leave it in RO/DI water for 24 to 48 hours before use. this will reduce the amount of phosphates leached by it. (Note some more than others but all carbons leach phosphate)
f) If possible use Ozone to break up the large organic molecules improving the efficiency of your skimmer.
g) Keep alkalinity between 10,5 and 11.5 dKH
h) Supplement alkalinity with Kalk in addition to Ca Reactor.
i) Vacuum as much as the Cyano as you can.
j) A loaded refugium with Chaetomorpha will also help reduce some of the nutrients.
h) If your PH is consistently low increase aeration. This will reduce the dissolved CO2 which also helps the algae.
i) I may risk flaming but if your sand bed is more than one year old (which yours is not) vacuum the sand as deep as you can and as much as you can reach (No need to go under the rocks) This action is specially needed if cyano grows on the sand surface and not only on the rocks.
It is my experience that most of the times we do not keep perfect sand beds. Excessive feeding, that cute Jaw fish or wrasse we can't resist can decimate the critters that the sand needs and as a result most often than not our sand accumulates lots of organics. You will not be surprised if you will be siphoning something very similar to skimmate out of the under-sand.
After this you can get a couple of fauna kits to replenish some of the critters and if you have a good functioning refugium I would not even bother with the kits.
j) Last but not least, keep your rock clean. No matter how much flow we will have, crevices, pores and holes will accumulate detritus. Regularly blow it off with the use of a power head so they can be removed by the skimmer. Corals love this as releases a lot of food and bacteria. every time I blow the rock my gorgonians and feather duster expand like there is no tomorrow trying to catch as much of the feast.
I use a MJ 1200 powerhead. get the tip of a turkey baster cut in half. Use the tapered tip as a nozzle for the powerhead to increase the flow speed and use your thumb finger to throttle the amount of water by partially covering the powerhead inlet as needed. Blow the rocks, put the tip against small holes and you will see all the stuff getting out. As a safety precaution, insure that there is a GFCI outlet were you connect the powerhead as you want to be protected against potential electric shock.
Once the slime is well settled and thriving you may find out that even reducing or fixing the source of the problem it will still be there and thrive as it seems to have a way of feeding itself.
This is were chemicals come into play.
Chemi Clean and Red Slime remover are both very safe and effective and by experience I can tell totally reef safe. It was also my experience that after their use I got a noticeable improvement in extension, color and growth from my clams, SPS and LPS corals.
Stick to the doses recomended and if possible try half a dose first before going full blown.
Chemi Clean seems to work by oxidizing the Organics while Red Slime remover seems to be some Erythromycin based compound.
When using Chemi- Clean during the treatment you need to remove carbon and any other adsorber (Purigen, Phosphate removers etc.) and turn off your skimmer. It is very important to increase your aeration because of the lack of the skimmer and because ChemiClean will use some of the Oxygen Dissolved in the water to react with the organics.
Right after the application your water will look like you dumped some kind of detergent. The more organics the more foam seems to be created. Also your ORP will drop to levels of 150 mv and will start increasing back on during the following 24 hours until levels way above what you originally had.
I will try using ChemiClean first. Compared with Red Slime remover, If Chemi-clean is a shotgun, Red Slime remover is a cannon as it seems to be a lot faster and more aggressive.
When using Red Slime remover you need to take similar precautions shutting down your skimmer and removing adsorbents. Upon application you water will turn Yellow green (First time I used it I got shocked by this so now you know what to expect). The discoloration will go away after 24 hours and there will be not staining at all.
The other thing you will notice is not a drop in ORP but a drop in PH so it is very important to start with alkalinity rather at the higher limit of the range 11 to 12 dKH.
In both cases prepare a good batch of fresh water mix. After the treatment you will need to make a large water change. of 20% minimum. I personally did two changes of 25% within two days after the treatment. This will insure that you are removing additional nutrient due to the sudden cyano die off.
Also to minimize this addition of nutrients due to the die off, try to vacuum as much cyano as you can before each treatment.
As a result you will get rid of the Cyano but notice that your water will be cleaner so other types of nuisance algae will also go away (My Chaeto stopped growing for about a month after all this) keep an eye on filter feeders (Feathers, Clams etc.) as many of them depend on organics. For a little while you may need to spot feed them If they were starving before the tratment, they will really need some nutrient afterwards as you may have removed much of it.