This goes back quite a few years, but long ago when I was having cyanobacteria issues, I considered using Chemi-Clean. But I didn't want to add it to a reef tank without knowing what the heck it was, and the ingredients were not disclosed. Searching through the web and the multitude of reef forums, the consensus was that its active ingredient was erythromycin (or some very similar antibiotic). I contacted Boyd Enterprises by email and requested an MSDS and information on the composition of the product. I was reasonably politely told to go pound sand, that the ingredients were proprietary. After a few very civil back-and-forth email exchanges, I asked if they would just either confirm or deny that the active ingredient was erythromycin. They declined to do so. I took their refusal to deny as a pretty strong indicator that the consensus was quite probably correct.
That's the background. And, although I had already bought the stuff and was at the ready to dump it into the tank, I decided against it and never used it. I did extra water changes, siphoned out as much of the cyanobacteria as I could when I did the water changes, and waited it out. After a few weeks it dissipated on its own, and has never returned in that tank, which has been running for more than 20 years. This tank has a 3-4" deep sand bed which has never ever been cleaned (by humans, at least). In almost all respects, it's your typical mixed reef, nothing terribly fancy for equipment, and I don't run reactors for GFO, carbon, calcium, or anything else. I have some of those reactors in the garage in case I ever decide to clean them up and sell them... along with a lot of other junk I didn't really need and will never use again.
My suggestion would be to try the simple things first. Advice is free, and a lot of it is worth what you paid for it (my advice is also free, btw). Go slowly but whichever route you choose, be thorough. Suggestions, of course, will tell you to turn off your lights, turn off your white lights, stop feeding the tank, run GFO, use Chemi-Clean, buy a new skimmer, test your No3 and PO4 eleven times per day, add macroalgae to your sump, acid wash your sand, nuke your rock, and stand on one foot while howling at the moon for 6 minutes on November 17th. Some of those might actually have some merit, particularly the last one.
I can tell you that you don't need to do twelve different things at once.
Be patient, be thorough, don't look for the quick solution. The resolution will take some time, but it will happen if you just stay on a reasonable course.