So I sent it back and went back to my old TiBook for a time, but have been desperately waiting for the return of my laptop. After several days had passed I was motivated to see if IBM had any way of telling me the status of my repair request. It turned out this required the serial number which I'd forgotten to write down. Thankfully some desperate searching through my browser history turned up the page I'd used to see what my warranty status was--which required the serial number.
This revealed that DHL had attempted to deliver the laptop that day, and hadn't left any notice that they had. (They might not have been able to find my laptop).
So I decided to work from home until I got the laptop back.
Of course when I looked at the delivery page, I discovered they'd attempted to deliver it before I woke up. Hopefully they'll try again today.