I've been fighting cyano for quite a while and am finally making good progress. My tank is 7+ years old and I used to feed fairly heavy. My skimmer was so-so as well. Over the years, the organics have built up in my sand and rocks to the point no matter how much flow I had, how little light I used or how many water changes I made, I was swimming upstream.
I upgraded my skimmer, and have removed the oldest rock . I'm stirring sand and doing filter sock changes every other day. I'm still doing fairly heavy WCs, but I'm convinced the bad stuff was locked up in my older rock and sand bed. I now only have little hints of cyano about once a week (still have a couple of rocks to remove).
Some of the rock I took out, I acid bathed, then beach soaked, then RODI soaked, then sun dried. Two weeks in to curing, the PO4 in the tub is .07. Coincidence? I doubt it, but I feel solid on this observation.
BTW - the pic of your zoas is exactly what was going on with me. My LFS owner told me that cyano is related to the red tide organism and will irritate corals, and that's why they ain't happy.