6x4 is 24 sq feet. 24 sq feet is good for about 6 birds. But the 24 sq feet should not include nest boxes. So you should deduct the nest box sq footage and plan accordingly. Go with a minimum of 4 sq ft per bird. Your run should be 10 sq ft per bird.
They might want to roost on the top of the nest box. You can add an angled surface to the top of nest box to keep them from going up there. I'm not sure if they really matters to you or not. Its not that big of a deal except for more areas to clean.
Keep us updated with the final pictures. looks good.
Being from GA, you can get away with less sq ft in the coop because the winters are not that bad, The food and water would have to be in the outside run, which is ok as long as you can keep the food dry. The roosts are a little restrictive for large fowl due to the lack of height above floor level . I see this as the main problem. Also, if you were close in the area under the coop, it gives you more than enough space out of the weather. As long as you make sure it stays dry . You could underpin with tarps or tin during the winter months and open it during the summer.
The roof will not hinge, but I am going to put a removable try beneath the roosts so I can take it out and clean it easily. The nesting boxes are pretty easily accessible. I am still thinking of ways to make it easy to clean, as it seems to be the biggest hurdle with the design for me.
Ventilation has not been added yet. There will be vents on either side towards the top. Also, the overhang of the roof on either side has a 6" -7" gap about 6 ft long. I am going to close this up with hardware cloth but leave it open for air flow.