As someone who's battled my share of cyano over my reefing career, here's what I would say:
First, absolutely get more CUC, as has been suggested to you. What hasn't been stated, is that you need something that is going to agitate the sand. Whether that's a healthy population of nassarius snails, a fighting conch, or some kind of sand-moving fish - the sand needs to get moved. Cyano blooms whenever it can grow unmolested, so make sure you're not giving it the sand as a safe haven.
Second, figure out what has caused the cyano outbreak. This might take a few attempts, as any number of things can let cyano grow out of control. Is it a lack of micrograzers? An excess of nutrients? Stagnant flow? Poor lighting? It might take a few tries to isolate the cause, or there could be multiple causes. But regardless, you need to figure out the root cause and attack that.
Finally, Chemiclean. Sometimes cyano does just go away on its own, but sometimes it is absolutely stubborn and will not go away no matter what you do; in some ways, it's self-sustaining. Once you have the cause figured out, don't hesitate to run a course of Chemiclean. Follow the instructions religiously, as it isn't a risk-free treatment and those instructions are designed to minimize that risk.
Chemiclean will absolutely knock out any particular infestation of cyano, but if you don't address the root cause it will come back. It might take several rounds of experimenting, followed by a round of Chemiclean, to finally knock out the cyano. Also, be aware that if you knock out a large growth of cyano with Chemiclean, it will liberate a large amount of nutrients into your water; those nutrients can easily fuel a secondary algae infestation (usually of bryopsis or GHA).