I haven't read all of the above posts but I remembered that the Passporter had something about Wheelchair rentals from OFF-Site. So I looked it up and there are two medical supply companies that deliver stuff to the resorts. Here are their numbers and their web sites, maybe they can help you to get the distilled water. Also try to see if the resort can accommodate you. I am sure they have had this question before.
Care Medical (800) 741-2282 or
http://www.caremedicalequiptment.com or Walker Mobility (888) 726-6837 or
Orlando wheelchair and scooter rentals-serving all Central Florida attraction areas-Disney, Universal Studios, Sea World, Kissimmee-Walkermobility.com (this one might be strictly for wheelchairs but its worth a try!
Good luck and I am happy to hear you have a new lease on life!