I a run of red slime, I have to keep it blown off my LR all the time. I have done water changes and used some phosguard but the Phos are not that high. .02
The tank has been up a year now and everthing is growing and showing nice colours.
I had the same problem recently. Try NO CYA NO from pet wharehouse. I followed the insructions exactly. I almost stoped after a week because I thought it was getting worse. Then all of a sudden it started going away until it was all gone. I put my carbon back in and turned my skimmer back on and it hasn't shown up at all. This stuff worked. 1 bottle for a 110 + 40 gallon sump worked good for me. I bought an xtra bottle that I thought I needed but I'm sending back.
Silicates may be the true culprit. Phosphates will only make things worse. What kind of water flow do you have. Cyano loves areas of slack water flow. If the nutrients remain in one place for too long the cyano will have a constant food supply.
Alf Neilson suggests raising your PH to an 8.5 - 8.6 for about a week and it will kill your cyano. While this is going on remove the cyano and limit nutrient input.