You have a really bad combination of things happening here. And the fact that your Phosphate reading is 0 is a perfect example of how phosphate is bound up in the algae and giving you a false reading.
That is darn close to a dinoflagellate outbreak. You have several steps that will help.
Manual removal - pinch it off and pull out. Dip your hand in a bowl of water, reach back in and pull off more. Repeat, always rinsing your hand to avoid releasing any back in your tank.
Siphoning - try to siphon out all you can. Using 3/8" tubing, you can limit how much water is wasted.
Chemically - I would use ChemiClean to kill off the cyano bacteria that I believe is present as well. Run fresh carbon on the tank for 3 days. Replace it at that point and run it again for another four days.
Reduce lighting - Either leave them off or turn them on for only 2 or 3 hours a day, if you have livestock that needs lights.
Water change - plan on a 50% water change during that week.
Biological - add some Turbo snails to help clean off your tank.
Stop feeding if you can avoid it for a few days. Only feed if you absolutely must, just a little bit to keep the livestock from total starvation.
