I would add some Nerite snails or small hermits to help control the cyano. It sounds like you are doing everything else right. They will also help clean up the hair algae. The nassarius don't need to be fed. They will scavenge on leftovers. Cutting back on your light will not really have any impact on the cyano. Normally I would recommend additional flow to help control cyano, but I know that's not a problem in your tank. Majke sure your skimmer is dialed in and you are getting the most you can from it. IMO the CPR's performance is only marginal, at best, for a tank your size. Getting the most out of it is going to be very important to maintain nutrient levels and also control of nuisance algaes.
Gary
125 SPS, 75 gal. LPS/softie reef, 9 gal. Nano