Insulating your roof hopefully will alleviating your problem I have kept as many as 24 birds in my 8'x4' METAL coop with no issues. Warm air is rising in your coop and condensing on the cold metal roof. Insulating the roof will rectify that problem. At lease it did in my metal coop. Just a heads...
You could easy remedy your problem on the roof with a good bonding agent to stick your Styrofoam to the metal and then in turn stick something to protect the Styrofoam from the hens devouring it. I never bothered with a vapour barrier and it worked out OK for me. Caution some bonding agents will...
This is my metal shed (it was given to me after it blew away in a wind storm) I insulated it with 2 inch Styrofoam and covered it with the veneer off of old interior doors from Habitat for Humanity (hens eat Styrofoam the same as we eat pop corn). It is cool in the summer time when it counts. My...