Coop space is only part of the equation. What counts is total space and when it’s available. It doesn’t matter if that is in the coop, coop and run, or they sleep in trees and free range. If your run is predator proof to the point that they are always able to access it and your climate allows access year around (or you protect it from high winds and snow to the point they can always use it) you should not have any space problems. You’ll probably have to do some work on poop management especially under the roosts. You can get my thoughts on space if you follow the link in my signature.
The coop height is a concern. The roosts need to be higher than anything else you don’t want them roosting on or in, like nest boxes. They poop a lot at night and you don’t want that on your eggs. Also in Ohio you need pretty good ventilation up high in the summer. Heat is more your enemy than cold. Heat kills a lot more chickens than cold. In winter you need some ventilation over their heads but you don’t want a direct breeze hitting them. That’s going to be hard in that coop.
Have you considered putting the nests in a totally separate structure? There is nothing that says the nests have to be in the coop.
The coop height is a concern. The roosts need to be higher than anything else you don’t want them roosting on or in, like nest boxes. They poop a lot at night and you don’t want that on your eggs. Also in Ohio you need pretty good ventilation up high in the summer. Heat is more your enemy than cold. Heat kills a lot more chickens than cold. In winter you need some ventilation over their heads but you don’t want a direct breeze hitting them. That’s going to be hard in that coop.
Have you considered putting the nests in a totally separate structure? There is nothing that says the nests have to be in the coop.