Are they on a roost when above the Lays boxes? I think this is a prefab coop, and they told you that many birds will fit, but they won't. It worked well when they were tiny chicks, but they are rapidly outgrowing this set up.
You really need to either reduce your flock, or build a bigger coop.This is going to cause a lot more problems than not roosting, but their not roosting is due to the lack of room. Adult birds need a foot of space for each bird on the roost. Your birds are not adults and have considerable growth yet to make. There is not room for them to even turn around now.
With winter coming, that is going to create a lot of moisture, their heads are close to the ceiling, moisture is going to collect on their heads and you will have frostbite.
But the worst will be the very ugly behavior you will get as the flock tries to eliminate birds to ensure themselves room in the coop. I am counting 8-9 birds, you should have a coup measuring 6x6 feet, or 4x8 feet. Your ceiling should be a foot of empty space above their heads, with good ventilation.
I think your coup is 4x4= 16 square feet, about enough for four birds. If you cannot come up with a shed or some bigger coop, you should sell half your birds. Sell them as point of lay birds.
Mrs K