In case anyone's interested, I finally got my Wii back today (from the time I shipped it to the time I got it back, it was 18 days). Or, to be more accurate, I got a new Wii today. They sent me a replacement one with a "post Wii repair instructions" sheet with the following boxes checked:
"After thoroughly testing your Nintendo component(s), we could not duplicate the problem you were experiencing. Your Wii and your Wii Remote(s) may need to be synchronized if both were not sent in."
"While we were unable to duplicate the problem, we have replaced the component(s) that we feel may fix the problem you described. All system data was retained, so no additional steps are necessary."
"Due to the nature of the problem you described, we have replaced your system. Your user information, which includes game save data, system settings, etc., has been loaded into this system. Depending on the system features you used, you may also need to do the following.
+ Your system has a new Wii number. If you had people listed in your Address Book in the Wii Message Board, they will need to be given this new number.
+ If you had acquired any games or applications through the Wii Shop Channel, these can be re-downloaded to your Wii, at no additional cost.
+ Any Miis you created are available on your repaired/replaced unit. However, these Miis can no longer be edited."
Sooo... that kind of blows. I guess I'm not surprised they couldn't duplicate the problem, since it only happened in certain circumstances, but if I'd known they were just going to replace the whole thing and I'd have to deal with a new system number and uneditable Miis, I don't know if I would have sent it in in the first place.
In conclusion, I guess my message to anyone else who encounters a similar problem is, just be advised: if the problem isn't easy to replicate, they'll probably just replace the whole system and it'll be a big pain in the ass.