I'm having the same exact problem, chatting with Apple Support now.

They referred me to their "specialized department" then ended the chat....... :D Guess we're stuck?

Very interesting. For the record my iCloud account is also very old and tied to a gmail address.

I fixed the problem but it's more of a workaround. Since having a gmail Apple ID is clearly causing the issue i tried logging in with the icloud email also associated with my Apple ID. I had no idea this was possible but it worked. :/ Wonder what other problems I have with icloud glitching out all the time is because of my ancient Apple ID.....