I found this article, followed the steps, and voilà! I can finally manage my music* on more than one computer. It’s amazing that you’d have to go out of the way like this to do something so simple as using your device the way you want, but at least it works now. Big kudos to whoever wrote this guide:
http://www.andrewgrant.org/2008/03/30/how-to-sync-an-iphone-with-two-or-more-computers.html
*One thing to watch out for: my Apps got ALL messed up (read: deleted) when I tried to sync them on the computer on which I wasn’t doing so before. I had to reinstall them all by hand one at a time since iTunes helpfully removed them all. So, maybe don’t try to sync them on both computers, just the music for now…
