Q: Apple ID password change zonked my phone's iMessage

The other night I changed my Apple ID/iCloud password, as you do. I did it on my iPad and let the rest of the devices think about it for the night.

Now, a month ago, I changed my wireless phone number. For some reason, the number change wouldn't "take" on my iPhone. Sending and receiving calls was no problem, but the phone number in Settings > Phone and Phone > Contacts was "+1 322 old area code old number". I'd change it manually in Settings > Phone, but it wouldn't last. And Messages would not activate even after a day.

But it fixed, somehow, when I plugged the iPhone into my Mac. I don't know what happened, but plugging it into the Mac, iTunes opened as it usually does, the new number was there, and it stayed, and iMessage and Facetime activated, everything was normal.

UNTIL I changed my password.

Now the weird "+1 322old area code old number" is back, and iMessage won't activate, and plugging it into iTunes doesn't change anything. I've turned off iCloud on each device and on all devices. I've erased and restored the phone, from Settings and via iTunes, set up as a new phone, restored from a backup both from iCloud and from iTunes, I've taken out the SIM card and operated it without one, put it back, did various combinations of soft resets and restarts, used AT&T's tool to reset the connection or whatever it does, nothing has yet worked.

Now, the phone itself is usable, and nothing else is affected; I get and receive calls and SMS to the new number fine. But iMessage won't activate. I've seen various web pages with weird strategies for getting iMessage to activate, but those haven't worked either.