As I understand it...

You CAN:
Transfer a FFXIV license to another PSN account.

You CAN'T:
Transfer an existing FFXIV service account to another PSN account.
Transfer characters from one FFXIV service account to another FFXIV service account.

I believe that if you need to switch your game onto a different Playstation or PSN, you're gonna have to deal with losing your characters.