Just started growing some green water in a glass jar, put it outside to get more sun but am thinking along the same lines as you with a light.
If anyone knows anything about the dark period requirements of algae I'd like to know.
I put some garden fertilizer in with mine and it has really taken off. Just used a water soluble garden fert at the minimum dosage.
Haven't given any aeration but plan to when I bring it inside. I couldn't be bothered with CO2
injection but you could give that a try.