Trouble with Google Play

I have come to the conclusion that I need to delete my old Email account. However, my game progress is linked to my Google Play profile which is associated with my old Email. I have tried to link a new Google Play with my new Email to my in-game account, but I keep getting an error that I cannot fulfill this action.

Is there a way for me to link my new Google Play profile so the old one can be dispatched?

Note: I have tried to reach out via the in-game 'EA Help' but I cannot figure out which options relate to what; basically making me stuck in a loop of confusion and futility.