If it was me, I'd stick with trying to hit good parameters and not dosing, honestly. Cyano is really easy to deal with by fixing whatever caused it to surge in the first place. Which water changes will not, if the problem is low nutrients and no competition.
You have a new tank, so you should expect pest algae. If you try to poison out every pest algae (or, in this case, bacteria), you're never going to get a balanced, mature tank. Cyano is one of the first algae-likes to turn up in most new tanks, and is going to stick around until something else surges to replace it. Then that's going to stick around for awhile. The ugly stage is inevitable, and the best way to deal with it (aside from getting ocean rock to avoid it in the first place) is to maintain reasonable nutrient levels, stock an appropriate cleanup crew, and ride it out. Eventually, it'll all sort itself out.