Per the article you reference, if you forget your recovery key, go to https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/ and select Manage Apple ID, log in with your password, and then change the recovery key.
I go to this page and enter your username and password after that I want to recover my keys.
I have already introduced the iPhone as a trusted device Kzdm but it is the same situation and can not get into my account.
The problem that exists right now, and I can only buy the iPhone because I do not buy any other device to retrieve the recovery key to.I was stuck in the same situation.
If anyone has a solution please help me.