I don't think you are crazy, but it will be a challenge. I hope you will post after your cruise to let us know if you were successful.
I am right with you on that free souvenir idea! Don't overlook the trading cards that they hand out at various places. I found that if we asked, sometimes we would get them in unexpected places or extra copies (great if you scrapbook!). I also kept all of the children's menus, which have a picture to color on one side and the menu on the other. I would ask for extras of those so I could keep their art work and a copy of the menu.
Unless you are a big photographer and really sure you are getting some great pictures, I think your biggest temptation may be Shutters. Even though my DSs were older (8&10) and I didn't see any candids of them, we did buy a few of the posed shots with the characters. From what I've read on these boards, I get the impression that the photographers take a lot more candids of the little ones.
While I agree it's nice to be able to vacation without worrying too much about spending limits, I don't think it will make your vacation any less special to concentrate on enjoying all of the great stuff you are already paying for! While we spent over $100 on our 4-day cruise, it wasn't excessively so, and I think we could have easily cut out a few of those things (Bingo, arcade card, a drink or two) if our budget necessitated it.
Good luck and have a great time!