Well, it sounds like you found the answer, but when I had green water problems, I accidentally found my solution. I had had my light attached to a light switch (my living room is also a home theater, and the only room not my bedroom) and had obviously had it on more than needed. My tank got lots of hair algea, and the plants looked awful. I redid it, more plants, much much better filter, but then also more fish... I know.
I had a huge explosion of green water right before vacation, I was recommended one of those little food cubes for while I was gone. I don't think the fishes were interested in it much, but the snails were all up on it. Anyway, worried about the fish given that I had never used one before, etc... I rushed home after 5-6 days hoping they would still be alive... well a couple were looking a little malnourished (lucky they had a new spawn of their own babies to graze on; guppies) and the crazy thing was, the plants had grown QUITE a lot, and the water was crystal clear.
The only real difference was not feeding them (though I don't over feed, for sure) and having the light timer set to 6 hours on, the rest off. I also put a board in front of a window to reduce light leaking around the shades.
My seasoned friend said it was cause plants need nutrients more than sustained light, and algea needs light more than nutrients.