You are paying all this money and taking an XBox? Why not just leave it at home and not risk it? You say that it travels with your family, but why is it such a necessity? Maybe it would do your family some good to learn to live without it for a few days. Just a thought.
If you must bring it, you risk Disney confiscating all or part of it, and then it's on you to remember to pick it up at the end of the cruise.