You might try following the link in my signature below for some of my thoughts on space. It won’t answer your question but might give you a little insight as to what I think is important.
Chickens do not understand the concept of coop space versus run space. To them space is space, wherever it might be. It’s not a pure square feet per chicken thing either, the quality of the room is important. If they have access to that run when they are awake then you are in really good shape. If they are locked in that coop for a while when they are awake it’s still not bad.
Just like most people, if another chicken is crowding into their personal space all the time, some chickens can get irritated. Some chickens can handle that a lot better than others, just like some people can. The tighter you pack them the more likely you are to have some behavioral problems. The longer they are packed tightly the more likely you are to have behavioral issues. A lot of chickens can handle being packed fairly tight, but some can’t.
One way chickens have learned to live together in a flock is that if there is conflict the weaker runs away from the stronger. You may see some conflict as they mature and set up a pecking order, but once they mature conflict is pretty rare as long as they are all hens. It’s that adolescent transition phase where you have your risk and usually it’s not that bad. Another thing that can happen is if two chickens don’t get along, the weaker avoids the stronger. That’s where quality comes in as much as pure square feet. If the bully is in the run, the one doing the avoiding may be in the coop. If they are both in the coop, the weaker may be on the roost while the bully is on the floor. It doesn’t matter if the coop has 6 square feet and the run only has 4, it’s good quality because they can avoid when they have access to both.
If you integrate chickens, especially if they are younger immature birds, your need for space goes up. Same if you let a broody hen raise chicks with the flock. But once they get the pecking order straightened out, the need for that extra space isn’t as critical. It’s not a magic number type of thing, it’s a lot how you manage them.
For different reasons I’m always an advocate for providing as much space as you reasonable can, whether in the coop or the run. I don’t know how much snow you might get in winter. If you can keep the snow out of that run and that run is available to them pretty much whenever they are awake, your set-up isn’t all that bad. If you don’t keep the snow out of at least part of the run, a bigger run won’t help you there, assuming you get much snow. Of course I’d like to see more run space. I think that will help your work load in non-snow conditions. And it gives you a little more flexibility if for some reason you need to respond to a problem. I really like flexibility, it has a way of reducing your stress levels when you have to deal with something.
That coop is a good size for that many birds. You’ll probably be OK with that set-up but with chicken behaviors I can’t offer you guarantees whether you expand it or not. Just don’t add any more chickens.
