Access by humans is a real issue on that coop.
I would suggest scrapping all of those nest boxes on the rear of the coop and making an access door on the back. Off to either side you could add a set of exterior nest boxes. Remove the second horizontal side board from the floor and build your exterior nest boxes on one or both sides. Use that 4x4 (or paired 2x4's) as the bottom level of the nest boxes. For a coop that size, you should only need 4 nest boxes total at most. Doing this allows easy access to your eggs and provides human access to the nest, and it would be at the perfect height o put your wheelbarrow under for cleaning out the duff. Right now, there is no access suitable. I think this would be the most straightforward method, and you might be able to reuse some of the nest box material. You'll also gain about 12 cubic feet in your coop.
For the roof, toe nail 2x4's on end and extend your eves. This will all a space for additional ventialion and provide an ovehang for your exterior nest boxes where they meet up with the sidewalls.
Otherwise it is a sound build, and I also like the shop, as it is VERY well lit.