I agree salinity is one of the most important parameters for a tank with invertebrates.
Info on the other parameters, particularly PO4( inorganic phosphate) would help too.
Depsite the low feeding and mechanical, chemical and biological filtration you have going on,the tank could have high PO4 which gives the cyano the nutrient it can't make by itself. Often rocks and substrate hold inorganic PO4 and leach it back over time . Keeping the PO4 low in the surrounding water for a period of weeks to months allows the surface bound PO4 species , to equilibrite with the water and ultimately exhaust. Running a PO4 remover such as gfo should help.