I've had a similar issue. Auto renewal failed for the domain used by one of our hospitals 6 days ago and we didn't realize this until our entire hospital lost external email access on that domain yesterday morning. The phone number on the account is the primary external number for the hospital and can't receive an SMS code so both my two factor options on the owner account are unusable at this point.
That's okay, all is not lost because when we set this up we were smart enough to make our two GoDaddy accounts delegates for each other, we're not totally stupid. Log in with the delegate account which can two factor successfully (since it's using a different email domain that has a staggered renewal date) and.... find that delegates can't process the renewal. Kind of begs the question why you would have a delegate who can delete your domain but can't pay for it to be kept intact...
Called CIRA as we deal with them directly on a lot of solution (it's a .ca domain) and they investigated for us and confirmed that while we're still in the grace period for some reason GoDaddy decided to get a head start and revert the name servers to default without telling anyone. Called back to GoDaddy support and after accessing the account with the delegate we go find that it's not authorized to request the name servers be reverted to what they were 40 hours ago, since it was an automated change GoDaddy triggered based on the auto renewal payment failing.
Again to be clear, I'm not requesting NEW name servers as that would be understandably sketchy, just trying to revert GoDaddy's change so I can successfully two factor the primary account and process the renewal.
I've called in about a dozen times over the last 24 hours trying every angle I can think of to get us back up and running but the circular logic is killing me. Definitely a lot of lessons learned for our other account but that's not helping the hospital that's gone dark.
I submitted the domain recovery request yesterday and included the renewal failure notice as well as the documentation of when we originally transferred the domain to the account so now I'm just waiting.
Hopefully
@James Iles is working today... I need some help in the worst way.