A couple of options:
1. It looks like you are still outside of "penalty" to cancel or change your booking and not be assessed any penalties. So you should be able to cancel with CCL and book with Princess to take advantage of this promo.
2. Call Princess first though. Verify that they sail from San Juan for the itinerary you want. Princess is a sister company of Carnival, but they operate as separate entities.
From what I understand, this promo you received from Princess is not valid on anyone but them. Carnival might not even accept it, but who knows. It doesn't hurt to find out. Call Princess see about their itineraries, ask about the promo coupon rules, transferrability, etc.