Question about your coop design, which I love by the way. What is the Black Jack #57 used for? Sealant as bug deterrent?That's optimal so the bird is never out of sight of the flock, though occasionally folks have had super stubborn broodies where maybe a change of location is needed to break them. But that's a fairly rare scenario.
A broody's hormones (which in turn affect her behavior) might cause the flock to treat her oddly, or vice versa, but as long as she's remained in sight of the others that shouldn't cause more than some minor skirmishes. I've had sick birds caged up to 6 weeks inside the run, and been able to simply turn them out and they rejoin the flock with almost no fuss.
Nice job on describing your design; the pictures are helpful and I like the descriptive details on the run build.