Well, I ended up getting a replacement unit for my misbehaving 10 Gb iPod. After sending it in for service and getting it back in not all that different condition, the nice folks at the Apple depot told me to take it and my case number to the local Apple store and tell them what happened.
They were reluctant to cough one up but I was more persistent than that. The Genius bar is pretty busy and in the grand scheme of things, this was rather low on their list of things to hassle with.
So I have a new one to play with. Among my lessons learned? Get some kind of skin for it so it doesn’t get as scratched up as it’s predecessor. None of them are very appealing: I’m not buying leather (unless it comes from windfall cows), so my options are rather limited.