recover account

With a Trusted Phone number, you should have been able to reset it using the Apple Support app on a friends device or the Apple Store. This is from the Support Page.

If you forgot your Apple ID password - Apple Support

If you don't have an Apple device but have access to your trusted phone number, you can borrow an Apple device from a friend or family member, or use one at an Apple Store.

1. Open the Apple Support app on the borrowed Apple device. If needed, you can download the Apple Support app from the App Store.
2. Scroll down to Support Tools, then tap Reset Password.
3. Tap "A different Apple ID."
4. Enter your Apple ID. If you don't remember your Apple ID, you might be able to use your email address or phone number.
5. Tap Next, and follow the onscreen instructions to reset your password.

In addition as noted in the Account Recover page, the process may be quicker if you can respond to a link sent to your Apple ID email:

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

In some cases, you might be able to speed up the account recovery process or reset your password immediately by verifying a six-digit code sent to your primary email address. You might also be able to shorten the wait time by providing credit-card details to confirm your identity. If you’re given this option, an authorization request goes to the card issuer.

Not sure what factors led to your long wait time or why you had to wait a month for your Apple ID. I thought you had your Apple ID, which would have been the email address associated with it. In any case sorry you have had to wait this long and it is not the experience that most users have to go through to reset the Apple ID Password. The process is usually pretty straightforward and is done by many every single day.

Unfortunately I think waiting the final 10 is probably the best approach to let the process play out. There is this warning in the Account Recovery support article:

• If you submitted your account recovery request with iforgot.apple.com through your device's browser, you should avoid using that device during this period. Using that device might cancel account recovery. 

Using iTunes to reset your device requires your Password, so that would not be an option. Sorry I could not be more helpful and like you, I do not understand why you are having to experience that long of a wait time.

In the future, the use of a Recovery Key may be a solution if you do not have another Trusted Device to reset your password. This is an optional security method, but if you lose your 28 digit Recovery Key, you will lose access to your Apple ID permanently. So it does come with some severe risks, but allows resetting the password without a Trusted Device if you have the Recovery Key.

Set up a recovery key for your Apple ID - Apple Support

• Do you have another Trusted Device?
• Did you have a Trusted Phone number set up?
• Do you have access to your Apple ID email?