I JUST finished dealing with that problem. In fact, I was just adjusting my skimmer to help clean up 15mins ago.
My infestation looked exactly the same, neon green, easily blown off (ie. not attached to the rock/sand) and grew back in two days. I borrowed a microscope and found out that it was spirulina, a type of cyano. I had already seen some damage where it head grown over my corals and my zoas all looked like green puss. I decided to go for a 2 day 'lights out' program overlapped by Chemiclean. I have a 180g SPS dominated tank that's one year old.
Here's the exact steps I took:
Friday: Filter socks changed and blew off the rocks
Saturday: Blew off the rocks/sandbed again. Unplugged my lights at Noon.
Sunday: Turned off carbon, UV and took the cup off my skimmer so that the neck would overflow into my sump. Dosed Chemiclean powder exactly by the instructions at 4pm.
Monday: Sat and waited while trying not to freak out. Turned lights back on in the evening (just blues).
Tuesday (yesterday): Turned the lights back to 100%. Turned UV back on. Turned carbon reactor back on and added an extra bag of Red Sea carbon to sit under the overflow pipe. Did a 15% water change and vacuumed up as much of the sand bed crud as possible.
Wednesday (Today): Super excited! Not a spec of green left and my sand bed looks better than it has in 6+ months. I'm slowly adjusting my skimmer to stop overflowing (valve on airline and pump turned all the way down) so I can hopefully start pull the rest of the crud out of the water.
Zero corals were harmed and my RBTA and fish are all happy as ever. I'm pretty sure my problem was due to neglect. I was terrible at doing water changes and had never vacuumed the sand bed. I ran vodka/vinegar on a dosing pump but had forgotten to refill it for a few weeks. My nutrients used to read zero Nitrate and zero PO4 but had jumped to 5ppm nitrate and .1 ppm PO4 about 10 days ago. The jump in nutrients and the ugly looking sand kicked me in the butt and I did a whirlwind of maintenance. I topped up my vinegar/vodka, cleaned half my sand bed and stirred up a ton of gunk, and I dosed Vibrant Cleaner in a hope to knock some of the algae and green slime back. I'm pretty sure that it was too much, too fast and my flurry of activity just fed the problems that had been building over the past few months.
Now that the tank is looking good again, I'm getting back into a regular routine. Daily water changes by my peristaltic pump, weekly sand vacuuming of 25% of my sand bed, change my filter socks every week and my carbon every 2 weeks. Most of all, I'm spending a minimum of 15mins every day watching my tank, nitpicking the cleanliness, inspecting equipment and generally just sitting and watching.
So ya, that's what worked for me. I'm still obviously just finishing dealing with it but I feel prepared to keep the tank looking good for the foreseeable future. Best of luck in dealing with your problem, I hope my experience helps.