I was able to extract my data and copy it to a disk image with the help of http://code.google.com/p/iphone-dataprotection/wiki/README. This process is really only appropriate for developers, I regret to say, but for developers the process is reasonably robust. I still had to read between the lines in one or two places, and make good use of the shell, but I am delighted to have retrieved my data from my iPod.
A lower priority question for me is whether to try to collect my notes and contacts from the assorted .sqlitedb files. It looks like iFunBox may come in handy if I try to push things back onto the iPod once I restore it.
For anyone who cares to know, my iPod Touch decided to listen on port 2000 instead of port 2222, my /dev/rdisk0sXsY devices had different numbers than expected by dump_data_partition.sh, and I had to find my keychain-2.db file in /mnt2/Keychains on the data filesystem. But it worked, and that's awesome.
After extracting my data, I tried and tried to restore the iPod, but was unable to from my 2007 Mac Mini. I finally tried from a PowerBook Pro running Lion, and was able to restore to a working iOS 6.
I had a few difficulties when trying to push recovered data back to the iPod. iFunBox allowed me to restore everything belonging in mobile/Media, which was great. But even in Raw File System mode, it won't let me access mobile/Library, I think because my iPod isn't jailbroken.
So I used the iphone-dataprotection approach and copied certain files back into place with ssh, and was careful to change ownership of the files back from root to mobile. At this point, I think all of my data is back in place, but the Contacts app still shows an empty list. I'm going to try sync-ing with my machine at home to see if that clears up the problem. I also had to reset all of my settings, since I have no idea where that data is stored, nor how to update it.
Correction: After making sure that the ownership was set to "mobile" for everything in mobile/Library, the Contacts app now shows everything correctly again. The only part I was not able to properly recover was all of my preference settings, and I have now updated those manually.
In short, I used iFunBox as a convenient way to restore everything that it gave me access to in mobile/Media, and I used ssh to restore everything in mobile/Library, taking care to change the ownership from root to mobile.
Using ssh is a mess because it first requires the process described in http://code.google.com/p/iphone-dataprotection/wiki/README. If iFunBox were to expand their access to include mobile/Library, that would provide an easy way for most people to recover from the kind of situation I experienced.