Phosphate is not really a factor in cyano blooms. Cyanobacteria only need nitrogen and carbon dioxide to live, and thus can thrive in relatively nutrient poor conditions. They are unlike algae, with the exception that they obtain their energy through photosynthesis. That's why you can have a thriving fuge taking up phosphates and nitrates, read 0 on tests, and still have cyano.
Like you I tried every conventional "fix". I ramped up flow and the cyano would still grow directly in front of a 2600 GPH Seio. I increased water changes, cut down the photoperiod, reduced feeding, increased alk to 11dkh, manually removed sheets of it, and still it grew all over my sand bed. (new tank, new sand, old rock) I just let it be for 8 weeks to try and wait it out, and still it grew.
I'm not sure what's in Chemiclean, probably potassium permaganate, a powerful oxidizer. Use as instructed if you try it.
I finally broke down and tried the Maracyn FW, it worked like magic, I had no losses in my tank except for the cyano. It didn't impact my biofilter at all that I could detect, and all the fish and corals acted like nothing new had happened. It does make the skimmer go nuts, and you will have to make sure your o2 doesn't drop from the use of it, aim a powerhead at the surface and then dial the skimmer waaaaay back. I waited 5 days and then started a series of 30% water changes. Cyano has never been back. If I remember right I only used 25 percent of the recommended dose on the package. I think it was 800 mg total spread over a period of 4 days, I added a tab a day for 4 days. (240 tank) I dissolved it in RO and added it to a high flow area. I dosed at lights out to take advantage of the fact that the cyano wasn't photosynthesising at that time. By day 2 there was a visible difference, by day 5 it was gone.
I think cyano thrives especially on new rock and sand until other nitrogen fixing bacterias can outcompete it. This may be why new tanks seem to get cyano while it is practically unheard of in matured set ups, unless something badly disturbs the biofilter, tipping the balance in favor of the cyano. Mine probably would have eventually disappeared after being outcompeted, but it was unsightly and growing up against some sand dwelling corals. This logic would also explain why it wouldn't grow on my rock which already had it's own high populations of nitrogen fixing bacterias and other organisms desireable in a reef tank. Just a theory, but it makes sense to me.
Anyhow, the Maracyn worked for me. Anyone trying the Maracyn, DON'T use Maracyn2!!! You can also use the FW Maracyn, it's quite a bit cheaper than the SW.
Just as a caution, a few people have reported crashes from the use of Maracyn and Chemiclean. If you wait this out it will probably disappear eventually. I'm just reporting what worked for me.
Good luck!