How to change back my Apple ID to @mac.com?

I always had my Apple ID as within @mac.com and made all backups using that ID

I recently lost my phone and I changed my Apple ID to another email, not within @mac.com domain.

I then realised that I am unable to see in my iTunes my hone backups I made before I lost my phone.

Now I am trying to change my Apple ID back to use my email@mac.com address and I can't!

It says:

You can only add the @mac.com address that is already on file in your account.

And I am unable to login to my @mac.com address because mail is asking me for Apple ID, which is already different.

Can someone advise me on how to get hold of my phone backups in such case? And how to recover my @mac.com Apple ID?

Thanks