So I ran across a tip that you can regrow your green onions indefinitely. I decided to give it a try, and here's what happened!
Day 1: Onions snipped above the whites of the stalks.
Day 3: Visible new growth.
Day 6: Several of the stalks have sprouted like crazy. They're growing at different rates.
Day 12: The stalks are as long as they originally were. Harvested a little already!
So the green onion regrowth trial worked just as well as everyone says. I'd say it takes about 2 weeks to regrow cut onions. I wonder how long we can keep this going? I may regrow a second bundle, so that we always have some ready to use on hand.
NOTE: After 3 cuttings, the onions got quite thin. I don't think you can go on indefinitely, but you can certainly get more onions out of them than one serving.