Apex legends - Playstation and Xbox cross-platform play from same EA account?

Hi, I'd like to play Apex Legends cross-platform between my Xbox and my PlayStation 5 in the same household.  Since both my PSN account and my Xbox Live Gamertag are linked to the same EA account, I understand that I won't be able to do this.  Can you please tell me how to change the EA account that is associated with my Xbox Gamertag? 

I've tried this:

https://answers.ea.com/t5/FIFA-17/Change-EA-account-linked-to-xbox/td-p/6168946

but each time I start up Apex on the Xbox it prompts me to add an EA account, but doesn't give the options to select an account, so it goes right back to the old one.