Definitely sounds like cyanobacteria to me. If you've done everything that you mentionb (low feeding, skimming, phosphate remover, and lots of water changes), you're pretty much into the "drastic" measures. One thing you haven't mentioned though is your input water source. Do you use tap? RO? Distilled? Something else?
If you are using an adequate wawter source with a confirmed low TDS, then you have 2 drastic options. First, a 3-day no lights period. Just like it sounds, unplug your light fixture for 3 days and cross your fingers. Corals will be ok with it, but often the cyano is not. And secondly, an antibiotic treatment like Red Slime Remover as a last-ditch effort.