I may have been too quick to celebrate the resurrection of my "broken" iPod. iTunes was doing something screwy and I had used another program to put some music on the device so I cleared the memory and went to start over using only iTunes. Big mistake. I've had nothing but trouble with it. I can't seem to get it to reliably write anything to the drive. I'm going to try the low-level format again and see what happens.
Update: It looks like the hard drive won't write anything at all now. It's listed on eBay. I bought it without knowing the defect. Now that I know the defect, maybe I can make a bit of profit on it. Or, at least, get back out (close to) what I paid. The good battery ought to be worth something.