Call Disney.
Several years ago, we had a in-room babysitter when our first princess was only 4. The lady was certified through Kindercare. I forget what the rate was, but it was reasonable.
Anyways, she came to OKW for about 4 hours while my wife and I went out and enjoyed ourselves at Pleasure Island & Downtown Disney at night.
I don't know if they'll have sitting services at such an early hour in the morning during marathon weekend.
http://www.kidsniteout.com/svcs_sitter.aspx
Our caregivers are available 24 hours a day, 7 days a week. Reservations may begin as early as 6:30am and/or may begin as late as 11:00pm. There is no limit to the number of hours that you may utilize the services of a caregiver. (During the Walt Disney World Marathon in January, reservations may be booked as early as 3:00am.)
Try these numbers:
Child Care at Walt Disney World
Tel

407) 827-5444 or
Kindercare - (407) 277-3424
Fairy Godmothers - (407) 939-3463
Cub's Den at Wilderness Lodge - (407) 939-3463
The Mouseketeer Clubhouses at The Contemporary and Grand Floridian Resorts - (407) 939-3463
The Neverland Club at The Polynesian Resort - (407) 939-3463
The Sandcastle Club at TheYacht and Beach Club Resort - (407) 939-3463
Little Toots at The BoardWalk Resort - (407) 939-3463