Counter service, ESPN Club, Big River Grille, Beaches and Cream. None of those accept reservations.
They could call and try a lunch or a dinner at some of the less than popular (but still good) places. Grand Floridian Cafe and Yacht Club Galley are good choices to start with.
We're avoiding the entire Thanksgiving dinner thing at Disney World. We're having our Thanksgiving dinner on Saturday night athe Biergarten. Much less of a hassle.