Can you arrange to be at a different park that day? We recently visited during Xmas week. We made a point to go to AK on Xmas Day and had a wonderful, almost leisurely day. We heard horror stories about MK and Epcot that day.
We always left our park of choice after lunch and returned most evenings to that park since we don't pay for hoppers. Even during Xmas week, we always got back in to our park around dinner time.
K