I agree, it is the run space that is most significant. Actually, in your climate with a big enough run, that coop would be fine. They can get by with 2 sq ft per bird in hot climates, where they basically use the coop only for sleep and laying, and maybe eating. Look over some of these warm climate "coops" (really pens) and see what you think. I believe if it were me I'd use the coop and put money into a run instead.
https://www.backyardchickens.com/forum/viewtopic.php?id=163417
https://www.backyardchickens.com/forum/viewtopic.php?id=163417