Ugh - sounds nerve-racking. I am sorry to hear that she is not interested in eating much - that makes it harder too. Maybe one thing you could try, that we had to do for a while was not give Novolog after meals. It meant more checking because we wanted to make sure he wasn't going too high, but for over a week he hardly went above 200 and even if he did, he was usually down into range a few hours later, he was at his Grandma's that week and was playing outside pretty much the entire time, so his activity was really keeping things in check. I'd be sure to discuss that with your endo, but maybe that would be worth a try, even if it is just for a few days?
The other thing to try at bedtime is a carb/protein/fat combo - not just a carb snack (like juice or fruit snacks). So peanut butter on graham crackers with milk, or ice cream :) or some cottage cheese and fruit. The protein/fat can help slow down the carb absorption and might help with the middle of the night lows. Do you have a dietician that you are working with thru your endo's office? They might also have some suggestions.
And maybe the pump would be a good idea. You can give really tiny doses that are much more accurate than trying to give 0.5 or 0.25 units with a syringe (our endo also said syringes are no better than 0.5-1.0 accurate unit either way, so with our kid's tiny doses you can think you are giving 0.5 and actually are giving double!) This why we are moving to the pump (well that and our son hates shots).