Oh gosh. I hate to be the one to give this news, but no, it isn't possible. I've had my deadname icloud account that's grandfathered in from @me.com for the last seven years. I did actually push this up the chain with technical support through a store, and there's a legitimate reason it isn't possible. The email and encryption is inextricably linked in a way that is impossible for them, on their end, to change. It seems like they got stuck with a bad design choice...

There is a slightly jank solution we have used for over five years now, as recommended by them. Create a new icloud account, with a new email address. Then create a Family with the two accounts both in it, and that will share all your purchases with both accounts. Sign into the new account on your devices and use that from now on. You do still see your deadname, but only very rarely.