Resetting password on a different email.

The only other way to get into the account is to remember the password and sign in.

The Recovery Process is an automated process and the length of time it takes can vary a lot. Apple ID Support can only answer your questions. They can't intervene in or speed up the process. The article below has some suggestions to shorten the the time the process takes.

Apple ID - Recover your Apple ID with two-factor authentication account recovery.   

I suggest you contact Apple ID Support for assistance.  See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. You may have to pick a slightly different problem.

Apple Support schedule phone call

https://twitter.com/AppleSupport.          People have posted it may take an hour or more to get a response.

From the Apple Support article below. 

Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.

Security and your Apple ID - Apple Support.      

Not if you are doing the account recovery.