Someone posted on another thread that local supermarket Goodings (goodings.com) charges $25 to deliver. They deliver to Bell Services, so you do not tip them.
Other suggestions:
Ordering from netgrocer.com, which supposedly has a selection of organic food and food for people with food sensitivities/allergies.
Renting a car for the day from Alamo at the Dolphin resort, and driving to a grocery store.
People staying at the Boardwalk resort go to resort's main entrance and cross Epcot Resorts Blvd; there is Hess Station with quick-mart that sells food and drinks.