Chemi Clean works! I've always avoided using chemicals to remove problems, but the cyano bacteria simply would not go away entirely. I'd lost a couple of frags to this algae, and done all the normal things to avoid fueling it any more. I cleaned the skimmer regularly, used a turkey baster to blow off the stuff anywhere I saw it, and even siphoned out what I could see on the DSB and rockwork.
Chemi Clean is a white powder that I measured to the tank's requirements and mixed in a glass of water. I poured it into the heaviest current of the tank, and turned off my protein skimmer for 48 hours. The slime algae faded away within one day, and after the two days elapsed, I restarted the skimmer. It pulled out about 4 cups of water within 2 hours, and that was it. The recommendation to do a water change was included in the instructions, but I didn't have time before leaving town.
I'm sold on this stuff, but plan to use it sparingly.