k so. phosphate test will possibly be useless but that stuff uses it to grow. you can go the iron route or the aluminum route. we can get in to the pros and cons of both at another time.
gfo is granular ferric oxide or rust you put in a canister as a medium to "bind" phosphate introduced to the system. (iron based)
seachem's aluminum method also works and i personally have never had an issue with it since it has to precipitate at 2.7 ppm at 8ish ph and you need 20+ or so to kill a sponge. (which leads me to believe the lower ph killed it in the test)
be that as it may. phosphate is your concern. maybe nitrate as well.
do a phosphate and nitrate test and get back to us?
I had the same problem and got a kole tang and he cleaned the tank up in less than 5 days. It was easily as bad as yours. This was after pulling it by hand brutally at least 3 weekends in a row only to have it constantly grow back. Never had a problem since....
Pull out what you can by hand and get a good clean up crew; turbo snails, hermit crabs, emrald crabs, and in my case a sea hare (an algae bulldozer). Using GFO as well to bring phosphate levels down and keep them there. Also stay on top of your w/c