Having suffered through the whole "kids & divorce" thing for many years, I have a few thoughts which may or may not help you.........
First, in hindsight, I think it would have been a better idea to sit down with your son and the ex and say, "So, I'm thinking of living on a boat, what do you both think about it?" Like it or not, you are in a partnership with your ex until your son reaches majority and her thoughts and opinions should be solicited and respected.
Second, do NOT be surprised if at the end, you find that your son has been going home and complaining to Mom that he really doesn't like being on the boat. He may not want to tell you directly as he doesn't want to disappoint Dad, but I would lay money that that's at least a part of the problem. Maybe a good talk with him is in order, and make sure you let him know that it's OK if he doesn't like it and that he should just tell you how he feels.
Third, if he's really all for it, most states allow a 13 year old to choose which parent he wants to be with. He should at least have an opportunity to speak with the judge and assure him that living on the boat while he's with you is just fine with him.
No matter what happens, it's a messy deal and I wish you good luck,
Mike, your response shows a lot of insight due to (unfortunately) experience and (fortunately) keen sensitivity to how kids think.
Time will tell.
Thanks for your good advice and your concern.