You know, in my climate, that chain link run with 3 walls and a solid roof over one end would be plenty of coop. Chickens tolerate cold way better than heat. There is a very successful coop design for northern climates that has a large open area on one side (I wish I still had a link for it, but it wouldn't meet your HOA requirements, anyway.) Where (in general, for climate) are you?
I think our climate here in Tucson is entirely too hot for something like the bungalo coop on MPC. It may be so hot inside that the chickens won't go in to use it. You would almost certainly have to remove one or two walls or at least significant portions to allow for ventilation. We need more ventilation here than in most places. I like your idea for the run, you just need some place within it for them to lay eggs and get out of the rain and wind. Like flockwatcher said, you don't need much more than three walls with a roof (most coops out here are just that). I recently helped an elderly friend here in town re-model her chicken enclosure to make it larger and so that she could walk inside without bending over. She only has a piece of awning with the roosts underneath. I think that in the winter she puts up plastic to block the wind, but they're fairly exposed. She's raised chickens like this out here her whole life. I only present this to show that chickens in our climate do well when they have plenty of air movement around them.
Here is the enclosure we made almost entirely of salvaged materials. Undoubtably, yours will be much more visually appealing.
