Ahh, this brings me back to my FW tank.
Green water = algae bloom (or let's say that's all I've ever heard of it being). In my FW experience, 1) doing bigger water changes will only prolong it, and 2) it's often triggered by high ambient light or oblique rays coming into the tank (ie: tank by a window). Whether or not that applies to salt as well I can't say, but it might be a consideration.
Are you familiar with Calfo's rant on algal succession (Reef Invertebrates)? The premise is that simpler forms of algae will take hold first and slowly do outcompeted and destroyed by more complex forms over time. Slime and hair algae are usually the first line you see (but hey, why not free planktonic algae too!), and then are slowly overtaken by "macro" algaes and eventually calcerous ones. By that argument alone I'd suggest you simply wait it out (I witnessed the process firsthand in my tank when it first got up to speed). Do a thorough set of water quality tests to make sure everything is about where you'd want it, make sure your source water is good quality, and tune your skimmer as best you can to improve waste output.
That algae needs to eat, same as everything else in your tank. If you deny them a food source they will starve.