Just to update for those with similar green water problems: I first tried adding plants and cutting off most light (a "brown out" approach), which did lighten the green color but didn't get rid of it.
So, as suggested, I rented a Diatom filter from the pet store. Man, those things work as advertised. It was a bit of a hassle to set up, but the water was crystal clear within a couple hours. Well worth the $12 they charged me to borrow it overnight and -- if I had multiple tanks or a bigger tank -- I'd seriously consider buying one for myself.
Thus far, there has been no return of the algae. The plants I added were of the floating variety again as suggested here, and I haven't managed to kill them yet. Technically, I believe it is the longest I've ever kept a plant alive in my home (other than the algae, of course).
Anyway, thanks again for the useful ideas; they actually worked.