Total time from my initial chat with a live support agent until I got the email letting me know that my unlock request had been approved was about 40 hours, which wasn’t bad considering the load they must be under.

So, well, thank you, faceless overlords at AT&T, for finally being decent sorts about the whole unlocking thing.  The next time I leave the country, it will be nice to just be able to buy a SIM card instead of having to buy a cheap mobile wherever I wind up.