I know Pizza Port has self serve beverages, like you said, and Rancho del Zocalo as well. WWS in the Grand Californian does. Hmmm... don't know about the new restaurants yet. Can't think of any others right now, maybe someone else will know of something I am missing.
Boardwalk Pizza & Pasta - the drink machines are self-service like Pizza Port and Rancho del Zocalo. BUT I asked the cashiers/CMs, on two different occasions, about the refill policy and both times was told they do not allow free refills. It caught me by surprise, as almost all quick-service locations with self-service machines allow for them.
Paradise Garden Grill - the beverage machines are behind the service counter similar to Tomorrowland Terrace and Pacific Wharf Cafe. I didn't ask, but just assumed that they do not allow refills since they are not self-service machines.