We ended up napping on the transportation.
The first day we spent in MK. The kids were nap ready, so we started to move towards the door. They fell asleep in the strollers. We got them to the boat (we were staying at WL), they fell asleep again on the boat. Ten minute boat ride later we got to the hotel. Moved to the room - and the ten minute nap was the kiss of death!
So we changed our game plan. Kids get tired, we get on the bus (the train in the MK, the monorail). One kid per adult, head on the shoulder. Kids fall asleep by the time you are out of the parking lot, and then you ride the bus in a circle for an hour or an hour and a half.
Its enough of a nap that they aren't cranky and make it to the end of the day. (It wasn't the best nap they'd ever taken, and staying up late for fireworks was not park of the program this way).
The parks closed around 7:00, except Epcot, which opens later and closes around 9:00. We never managed to stay up for Illuminations.