wildman:
you answered your own question.
First you know that cyano is an indicator of nutrient problems in your water. Use it for what its worth. Find out what, where, and why and correct this first. Be it over feeding, no nutrient export, too many fish, what ever the case maybe. To get rid of cyano you must solve this problem.
So w/ that said cyanobacteria is bacteria, which means you can eliminate it antibiotics. so i tell you that you can get a red slime algae remover (which is erythomycin) treat the tank for the required # of days and then remove the med (water changes and carbon). One concern w/ treating the tank is of course wiping out some of your biofiltration. So keep an eye on the water chemistry while treating.
Lastly, unless you eliminate the nutirnet problem, your cyano will come back.
enuf for now
frank