I'm battling cyano now as well, and have been told it could be any of the following factors:
not enough flow
bulbs need to be changed
high nitrates
any amt of phosphates
too many nutrients (ties back to nitrates)
I've been told that Queen Conchs or fighting conchs can wipe out cyano pretty quickly and without chemicals, so I am going to pick up a couple today. You may want to try the same. I have heard from a member of my local club that they tried the red slime remover, and even at 1/3 the recommended dose, she lost a bunch of her inverts - shrimp, urchins, starfish, etc.
I have also heard someone say that if you leave your lights off for 3 days, it will kill it as well. I haven't done this yet because I'm too afraid of the impact it will have on my corals, so I am going to try the conchs and see what happens. Hope this helps. Keep us posted with your progress.