The restore of my wife’s iPhone 4 finally took. I don’t know why, but it wasn’t working if I followed AT&T’s instructions of simply restoring the phone within iTunes.
This is the procedure that worked:
On the iPhone:
Settings > General > Reset and Erase All Content.
Don’t restore the backup just yet, instead set it up as a new phone, with a different name than before.
Once that’s complete, hit the Restore button.
After all that, I was greeted with the message I’d been looking for.
Now go ahead and restore the old backup that you made (you did make a backup, right?) before you started this whole have-AT&T-unlock-your-out-of-contract-iPhone pipe dream.