It sounds good to me. I'm envisioning a welded wire apron at least 18" wide. I think an apron is as effective, if not more, than burying it and is certainly a lot easier to install. Considering the hardwire cloth, I think 18" is enough, but whatever the width of the roll is would be what I would use. 18" will keep things from reaching through, keep the adults from sticking their heads through, and will keep young chicks in.
I'd also go with the welded wire above the hardwire cloth instead of chicken wire. It is just so much stronger. I use J-clips to connect two different wires but hog rings or weaving wire through can work too. Just don't leave any big gaps between the hardwire cloth or welded wire. You'd be surprised how small a gap a raccoon or such can squeeze through.
I like the 7 foot height on the roof. I think you will too. Just remember to slope it so the rain runs off away from the run. If you build a flat roof, the water will set on it and seep through.