We have the same issue, but for us, I think it may actually work in our favour.
Our daughter will LOVE the shows. That will be 100 times more interesting to her than a sit-down dinner.
So, it's most important for us that she is "awake" to see the shows. We'll get her "dinner" from the options around the pool (pizza and chips is okay on holiday) or Cabanas buffet either before or after the show. All going well, she might have a little something at our actual dinner (probably just dessert) and then - fingers crossed - go to sleep in the pram.
Of course best laid plans ... often go awry!
EDIT: since posting, I've learned that Cabanas is NOT open for dinner.