Adam Albright has the solution!
To look in the ~/Library/iTunes/Mobile Backups folder to find the Manifest.plist folder, and delete entries for apps that might be causing the problem.
I remembered that a little while ago, I had started getting an error message while syncing and updated app (Sleepmaker or something- couldn’t remember which, precisely, but knew that it was a white noise app). So, I went to the Manifest.plist folder, and removed the entries for the couple different flavors of the Sleepmaker app that I had installed.
Then, reconnected the iPhone, and clicked “Continue Restore” once again when it reported that there had been an interrupted restore. This time, it went through fully! Took quite a while (~1 hr) to copy all my media onto the phone, but now it’s all there! Hopefully this will help others who might in the same situation…
If you have Windows XP you may want to read this thread.
In my Windows XP the manifest.plis file was in this folder:
C:Documents and SettingsAdministradorapplication dataApple ComputeriTunesMobile Backups87XXX6HDXXK