I have yet to see chicken poop that would fall neatly through 1/4 or 1/2 inch hardware cloth, and chicken wire isn't real good for their feet. I know it sounds easy to have the poop "fall to the ground under the coop" but with your setup, even if that would work where would the poop end up? In your run section under the coop. You really wouldn't have saved any extra work because that area will get nasty real quick. So you are down to a couple of choices. You could go with your plywood and paint it with Black Jack, like so many others do. Easy to clean - hose it down. You could also by a linoleum scrap (those are usually really cheap) and put it down over your plywood for easy cleaning. Run it up the sides of the walls a couple of inches. Then put a layer of Sweet PDZ mixed with construction sand so you can just scoop out the poop - like cleaning a litter box. Again, think about how you will access the inside of the coop for cleaning.
You don't need that many nest boxes for the number of chickens your coop can hold. My 22 chickens (well, 19 now) use only 4 out of the 6 nests out there in their coop. With 6 chickens, 2 nest boxes is more than adequate.
Do you plan to leave the area between the roof and the wall of the coop open? If so, you can cover that with hardware cloth for ventilation. Could you show us a photo of the front part of the coop, maybe by standing in the run section and looking toward the coop? I'm a little concerned about the ventilation in the coop, but if you have more openings on the wall that faces the run that could make a difference in air flow in the coop as well.