I'm surprised at your choice to use drywall. I would think that plywood sheeting would be a more practical choice. I don't know a whole bunch about construction but we stored some drywall in our garage and over time the humidity caused it to deteriorate and mold a bit on the edges that came in...
That's looking great! Your chicks will love their deluxe accommodations for sure. My only suggestion is to skip the chicken wire and go with hardware cloth. As someone who used the same "I'll be there to shut them in at night" logic when building my run, I can tell you that's the thing I regret...