That mystery ship was the Norwegian Joy. I only know this because I was on that ship the same day in Cozumel. We saw all the other ships also when we went on our excursion. You had almost the same itinerary as us, Roatan, Belize, and Cozumel, but we had Costa Maya as well.
Great review! If you have to go back, I highly recommend ziplining in Roatan and Playa Mia in Cozumel. Is there anything you would recommend about Disney? This may need to be our next cruise (due to it being a family trip and their insistence on only this cruise line).