My iPod's Back! w00t!
So it does seem that it was the file system and partitioning that was causing all that hell. After I deleted the partitions, and formatted the drive as Fat32, the iPod Updater worked just fine.

I was a little worried; as the formatting was nearing the end, I got a message, "Windows was unable to format the drive." I was dreading that I would attempt to use the iPod Updater only to find that it would get another "Could not mount iPod" error. I was so glad when I saw that blue progress bar slowly inching its way across my screen.