Alex,
I know exactly what you mean about fighting sleep when life is interesting. When Katie was at that stage, we used to try and find a quiet corridor someplace and walk up and down until she was asleep. Obviously, that's not so easy at WDW, but there are some out of the way nooks and crannys, and some pretty quiet boring shows- someplace like the Hall of Presidents, or one of the Epcot moves might work well. We also used to put the hood up, and throw a blanket over the buggy so it was dark and very boring. That would be too hot in Orlando, but maybe a muslim cloth would be ok.
Pegasus - my dd also loses her appetite in the heat, even now and she's nearly 5. As long as they are drinking plenty of water I don't really worry about it - she nibbles on bits and pieces throughout the day, but never really has a meal. I figure she won't starve to death - if she is really hungry then she will eat.
Bev