How can I recover my Apple ID after multiple failures?

The people here are customers like yourself, not Apple.

Your Apple Account password and iCloud password are the same thing.

We'd need more details than around in circles, particularly if the genius bar person who had you right in front of him showing him things could not figure it out. Where exactly do you have problems?

This Apple article has instructions for what to do if you have forgotten your Apple account password, or the system does not recognize the one you remember —> If you forgot your Apple Account password - Apple Support

or go directly to this link —> http://iforgot.apple.com/

If you don't receive your verification or reset email, read this Apple Support article: If you didn’t receive your verification or reset email - Apple Support

"When you make certain updates to your Apple ID, we’ll send you an email to help you complete the update. For example, you might have reset your password, reset your security questions, or added a new email address to your account." Also check your junk mail.

If you find you can’t sign in, reset your password, or receive verification codes, you can request account recovery (read this support article: How to use account recovery when you can’t reset your Apple Account password - Apple Support ) to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. This is a multi-step process. More detail in —> Activation Lockout Issues - Apple Community and My Apple ID is locked, how do I fix it? - Apple Community

This page has telephone numbers for contacting Apple for support and service ➞ Contact Apple Support - Apple Support

If you are signed into this forum using the same Apple Account then your browser may be configured to automatically enter your password. You should be able to view stored passwords in your browser's preferences/settings.

CerveloR5 wrote:

Around in circles means being prompted to wait 24 hours, then being prompted to wait 3 days for a recovery process, both leading no where.

That is the standard Account Recovery process only required when you do not have another Trusted Device or Trusted Phone number already on your account to reset your password with Two Factor Authentication.

How to use account recovery when you can’t reset your Apple Account password - Apple Support

After you start the process, you get an email within 72 hours that will tell you how much longer you need to wait before you get a Text Message with the instructions to reset the password. This could take a week and the entire process will reset for any of these conditions. Apple cannot speed up this process or simply send you a reset link, that is never going to happen, all they can do is assist you by following those required steps.

• Regardless of how you started the account recovery request, you should turn off all other devices that are currently signed in with your Apple Account until account recovery is complete. If your Apple Account is in use during your request, your account recovery will be cancelled automatically.
• If you started your account recovery request with iforgot.apple.com through your device’s browser, you should avoid using that device during this period. If possible, turn that device off. Using that device might cancel account recovery.

Certainly returning your new phone is an option, but you will still need to gain access to your account at some point. After that has been done, you can purchase the phone again if you wish. At that time, make sure you have two factor authentication turned on and have a valid number entered on your Trusted Numbers to easily reset the password next time.

Did you check your spam folder for the email? If you are using iCloud for your email service then that is a mistake. They are sending email to the very account to which you have no access. Call Apple about that. In the long term, look into using a third party address for your Apple ID.

Since you say this has been escalated to higher levels at Apple, that is a lot higher than the people on this forum. Apple provides this site for customers to help customers and Apple is only here for moderation purposes. I'm not saying it is impossible that anybody has a solution for you but they would have had to have been in exactly the same situation, unfortunately. I suspect that most of the people who are actually on this forum to help others may have limited personal experience with most of the issues raised; e.g., I have never had a locked account.

If you are going through Account Recovery you may wish to read some do-s and don'ts in this article How to use account recovery when you can’t reset your Apple Account password - Apple Support