Apple has defeated me, for today.
Commenter ntetreau pointed me to an page in the Ubuntu documentation about syncing to an iPod Touch. gtkpod seemed to be working, it listed the movies I had synced earlier in iTunes as well as some podcasts that I deleted in iTunes a while ago. I deleted the podcasts, and synced an MP3 file to test it out.
Back on the iPod Touch, the music and video applications said “No content”. In Windows, iTunes reported that the iPod was corrupt and needed to be restored. That means re-jailbreaking, reinstalling all the apps, and re-syncing with iTunes.
Obviously I went wrong somewhere while following the documentation. It wouldn’t be such a complicated process if Apple would stop trying to force iTunes on iPod users by purposely locking out third party syncing applications. Or, port iTunes to Linux (or help Wine out with getting it to work).
For now (maybe until the next firmware update is hacked) I will continue using my iPod Touch with MobileCast, which downloads podcasts and video without a computer.