Ideally you don't want to feed many carbs after the nadir because the insulin starts to wane after that. Think of the insulin as a car slowing for a stop sign. Adding carbs may put on the brakes and stop the car prematurely, or shortening the duration.
It's fine to leave food down overnight and it's OK as long as it's low carb
The only time we don't want them eating is the 2 hours before pre-shot tests so the number isn't influenced by food.....if you can't pick up her food by +10, you might want to consider using an auto-feeder and having it open to an empty slot for that time
A lot of people use the PetSafe5 so they can let their cat have some food overnight but still control when they get it
The AMPS is always the number that takes the longest to come down due to something called "Dawn Phenomenon"