I don't understand what the issue is then. We only did lights out for a week, I dont think month(s) would be necessary to treat this. Really the lights werent to "treat" the problem, but rather to get it under control while the problem was treated with other methods.
My first thing to suggest would be to stop the chem-clean. I've dealt with cyano chemically before, but its important to note that dinoflagellets is not cyanobacteria, and in fact, despite being similar, is treated a little differently.
When you say you do a tank blackout - describe that. We actually wrapped ours with a black blanket in order to make sure as little light entered the tank as possible. But again, this was only to treat the symptoms not the problem. After the week of blackout - if we exposed it back to a complete photoperiod, the stuff would have come back because a week isnt enough time to remove the nutrients from the system.
I recieved a PM this afternoon from someone else encountering the problem, and I feel as though a rundown of everything we did is in order - though what I did I dont claim to work in anyone elses situation, though the half a dozen people who have used my method so far have made mention to me that it worked perfectly.
- we did the blackout to treat the symptoms and help keep the dinoflagellets from smothering the few corals that remained in the system.
- we then began the process of reducing the amount of nutrients in the system. This included skimming wetter than normal, as well as the addition of more macro algaes to the fuge. Water changes though seemed to make the problem worse, so instead of doing water changes, we put filter floss between the baffles of the sump and began blowing the rocks off with a turkey baster. The floss would capture the particles as they flowed through the baffles of the sump and be mechanically removed.
- we did use carbon, though I dont know if it did anything. Generally we always use carbon but change every other week, during the battle we changed it every day.
- We dramatically upped the flow in the tank which brought it up to the 20x turnover mark that you should be shooting for minimum.
- We also severly cut down out feeding regiment which, having used the new method for such a long period of time leads me to question what in the heck we actually were thinking feeding that much...
As stated earlier, the outbreak is symptomatic of an underlying problem, just like cyano, and if treating chemically does the trick, you still have to alter your habbits with the tank or you likely will have another outbreak.
Disclaimer: My methods worked for me. I guarantee nothing

I also do not want to come off as harsh, because that is not like me, and definately not my intent. I know that this battle can be won through dilligence without chemicals, and thats how I feel it should be done. Using chemicals is a personal choice that we've made before to treat symptoms in other tanks, however, for the 150, the only "chemical" we use is Joes Juice for treating aiptasia, and we really have never regretted doing that method.
As for the zeo or probidio, I dont know if either of those will fix the problem, however, if you are looking to "start over" I would say they ight be worth looking into. Hopefully you can find what's fueling it, but my reccomendation is to stop the chem-clean treatments as they can affect other things too.