When I first set up my tank, I had the same thing. I read these threads that kept debating between nitrates and phosphates. I tried reducing feeding almost to the extent of not putting any food in the tank.
In the end, I simply siphoned off the cyanobacteria as often as I felt like it and increased water flow. Eventually, it stopped coming back.
I have suspected that it was feeding off something in the sand or rocks and eventually used ups its food supply. Either that, or the increased water movement may have simply made it impossible for it to "stick".
Since the stuff went away, I have taken out two of my power heads and now only have one power head with the propellor modification in a 55 gallon tank. There are certainly some places in the tank that don't have great flow, but still no cyano. (perhaps the mushrooms, zoos, leathers, etc are eating the things that used to feed the cyano.)
In any event, just keep plugging along.