Thanks for everyone's advice and support lol I will do a lot more research on building a draft free house inside.
Is it horrible if they sleep aahs lay eggs in the same areas?
For your climate I wouldn't worry about building an actual coop - this open concept is much better for hot, humid climates. Only reason to actually build a coop is for additional security, or protection from driving rain/winds, but a coop/run combo can be made pretty secure, and if needed you can do partial walls just to block wind and rain from the section they'll sleep in.
You don't want them sleeping in nests - no one wants to clean poop off eggs. Put their roosts up higher than nests, and if you find them sleeping in nests, block them off for the time being until they get used to sleeping on roosts.