Do you have a picture of your sump? it is very possible you could incorporate a refugium in it.
I think with a 125gal tank you could put a yellow tang and not be too worried about aggressiveness, but of course that is up to you, Definetly start pulling that stuff out as fast as you can. And yes FL rock comes with a lot of macro growing on it, I don't think the tang will make too much of a dent in that, but once you get it to a smaller level it would help keep the algae in check.
Sorry I didn't mean to imply that you added the macro, I just hear Bob tellling everyone to put them in the display and I hope they will all see your thread and see how it can get out of hand.
Anothere option with a refugium is to set up a small tank next to the display, they can be neat looking also. I really do think that plant life is important to a saltwater tank, I just don't think it needs to be in the display choking everything else out.
once you get rid of some of that algae your cyano problem may go away, I always have had some slime in my refugium, because the macro slows down the flow in the tank, Looks like you have one large 125gal refugium right now.