This doesn't really answer your question, but it's an alternative to needing to have a case of water shipped. I bring a reusable water bottle to the parks (filled up at the hotel) and every time I get a meal, I ask for a large cup of ice water that I use to fill my bottle. Water from the soda fountains tastes a million times better than the water in the drinking fountains around the parks. The cups of water are free and I have had no issues asking for them. I even got one from a counter service place without ordering any food once.