I recently learned that if a customer has an account in CH associated with other stores, then they are NOT automatically added to my store.

My opinion is that a customer that already has a separate CH account (like with another store) should automatically be added to my CH store if they match one of my POS customer accounts by phone or email. If there is a conflict of information (like phone matches but email doesn't), add the customer to my store account and send me an email letting me know that the customer was added but that there is a conflict of information. That way, I can ask the customer what they prefer to do.