Per the Carnival site, the Ecstasy is 885' long (the citation didn't say if that was LOA, LWL, or LPP). That works out to ~2.5 feet (885/350). It is big, but doable. I'm assuming that you don't want the underhull ...
I think that I'd contact the public relations office at Carnival. Explain what you want to do and see if you could get a set of deck plans and some good exterior pictures. Size the deck plans to your desired scale via a Xerox and glue them onto some basswood of appropriate thickness. Cut out and lay up like a bread & butter sandwich. Sand smooth & fair the layers together. Skin hull sides, deck, & windows with Evergreen