Saga update:
Current status on the 12306 website is:
Document - not verified
Phone - verified
Meanwhile I installed also the Chinese 12306 app direct APK from 12306 CN (which installs in English - but you can switch back to Chinese)
Last time in China I had no time to go to the ticket counter for passport verification. So today I went to the High Speed Rail Station.
It has a (Low Speed) counter (actually 3 counter) service for buying tickets - and - wait for it! - document verification!
With 10 people in front it took only 30 Minutes. Actual verification took just 3 Minutes or so!
Very fast and smooth. Only issue - it's still not verified! I called the High-Speed-Ticket Hotline at 2120-0888 and they are looking into it.
...and called back a few hours later... They suggested to delete the account and do a new one. Deleting isn't actually that easy, so I created a new one. However, you can't created one with the same passport. Delete only (maybe) works with the app - but only the Chinese one.
What a bunch of incompetent twats, probably normal for China.
One unrelated issue: 12306 want's me to send a SMS with 999 in it to them - however, I get "Trouble sending" from my China number phone. It's a new phone, but in the past I could send SMS from HK to CN with now problem, like 10086 'ye' for a balance check. Any idea what that ain't working on the new phone?