Chemiclean is a nuclear bomb approach and it will not solve the issue, it will only give temporary relief, and also kill off most of the good bacteria in the tank which usually means cyano will come back even stronger within a week or two because now the tank will lack a major part of its filtration, which is good bacteria. I have lost count over the last couple decades on how many people I know that have wiped out their entire tank (corals and fish) from using Chemiclean because it strips the water of oxygen. Fix the source of the problem, don't just mask it temporarily. Heavy feeding, bad source water, and lack of flow and proper filtration are the main causes of cyano outbreaks. Any type of sponge filter should be rinse cleaned daily or else the food just rots and fouls the water. This is a major reason why canister filters are not recommended in saltwater, most people don't keep them properly maintained as most are a pain to clean on a daily basis.
As far as nitrate/phosphate readings, those are pointless when talking about cyano as cyano can grow very well in 0/0 conditions on a test kit because the phosphates it does feed on are organic phosphates, and we usually only test for inorganic phosphates. You will kill corals before you kill cyano if you strip the water of phosphates and nitrates. Cyano feeds on DOCs (dissolved organic carbon) and silicates more than it does nitrates and phosphates. My tanks have phosphates in the .50 range and nitrates in the 10-20 range, yet, I have never had any hint of cyano and that is because I have the correct flow and filtration methods to make sure the tank is cyano free.