I have a streamer friend that was able to put me in contact with a creator lead at Dice about two weeks ago and just wanted to let you all know that a potential fix for the issue has finally been found. The error is in fact EA account related, NOT STEAM, and explains why linking your Steam account to another EA profile works. It's also caused by having had multiple EA IDs on one account which isn't supposed to be possible in the first place as I originally suspected was the issue.
So I gotta unlink the Account from Steam and it will work?
If you unlink your Steam account from your EA account and link it to a brand new account then yes you should be able to play the game. Your stats and beta rewards if you earned them are tied to your EA account though and you'll be starting completely fresh. If you bought the Phantom Edition you will still have all of that stuff on the brand new account.
Didn't work
