How to resolve the Apple Account recovery issue and regain access?

For over three weeks I have been locked out of my account. Despite following instructions to recover my account, I am experiencing an endless doom loop. Even worse is that Apple Support - while very nice to talk to - is unable to help or to escalate the issue. This is failure of their system, and no way to get any help.

Three weeks ago went to change the password. The Apple system asked me not only for my email confirmation (which I provided) and my phone confirmation (which I provided), but also the login password of a laptop from 3 years ago. Since I get a new laptop every year, and change my password regularly, that was an impossible question to answer. When I couldn't do so, I got locked out and had to undergo account recovery.

Since then, it has been 23 days, 6 attempts that have each failed. I have the same email and phone number which I confirm each time, on the same devices, in the same location. And yet, it won't let me access my own account. I've had many conversations with apple entry level and senior support. They all give advice about how to make it work, which I have followed many times. But, it fails each time.

I have been an apple user since the Apple II in the late 1970's. I have purchased dozens of apple devices over the years. I have overseen IT at a large corporation and am sophisticated in my use of technology. I have now met multiple people who have experienced this. And yet, nobody has any idea how to solve this.

This is a defective apple recovery system - with no customer support that can help.

Does anyone have any ideas? Is anyone from Apple going to read this and try and help?

[Re-Titled by Moderator]

Original Title: Account Recovery Doom Loop