As it turns out, you cannot "switch" EA accounts on PS4.
Games requiring an EA account on PS4 will automatically search for one using your PSN email address, and if none is found, they will automatically create one and link it on your PSN account.
Try logging in on ea.com with your PSN email (worked for me while searching which account Anthem and Dragon age were using).
Like you, I have played many EA games in the past, some of them on PC (like Crysis 3) which required an EA account. But saddly this "PC" account cannot be linked to my PSN profile because it uses a different email.