Well, remember, cyanobacteria is VERY crafty. It can use a lot of different compounds as nutrients to help it grow. High up among the list are nitrates, silicates, and phosphates. Some strains can also use ammonia, and even more nefarious ones can use nitrogen gas itself. In my personal experience, a rapid removal of cyano is nearly impossible. The only "rapid" method is antibiotics, and using them is an absoloute LAST resort (cause you risk killing beneficial bacteria too). Unfortunately nobody has created/found a targeted baceriophage, cause that would be the ultimate dreamworld answer.
If your nitrates are still very high (20ppm+) you can consider either water changes, or using a nitrate sponge. There are a few different companies which manufacture a nitrate removing chemical. Basically looks like white gravel that you put in a filter sock or women's nylon, put some flow over/through it with a powerhead or airstone, and wait. Usually within a week nitrates are bound up in this material, and it is thrown away.
Nitrates CAN be the source of your problem, but so could silicates, ammonia (even undetectable levels are enough), or other dissolved organics you cant test for. I still maintain that doing waterchanges (with RO, tapwater wont help), once a week and vaccuming it up directly using a thin-hose tubing over the course of a few weeks is the best way to conquer it. Basically allow it to grow and consume its nutrients, and when it runs out, it doesnt come back. Mine came at about week 6 of my tank. It's spread was halted by those methods on week 8, and by week 10 till now there has merely been trace amounts of cyano. Patience is the best treatment.