Thank you all so much for the great advice! I will remove their roost and food from the outer cage. They free range during the day though so we will just have to make sure they have plenty of food and water inside their coop. They have been sharing the caged area with the rabbits so we will have to move them for this to work I think.
We are going to make some changes to the coop before we start this though. My husband built the coop out of pine fence pickets and the inside is plywood. He is going to remove a picket on the east and west sides of the coop and replace it with stacked Plexiglas so they have permanent windows instead of using a light out there.
I really really appreciate how incredibly helpful everyone on this forum is! This is my go-to place for chicken questions