I use commercial rubber roofing. It's very thick. I know you are short on time, but in the future, if you are driving around and see work being done on a large commercial roof, just ask one of the workers if you can get the stuff they are tearing off. They have to pay to dumpster it and have...
You are probably right.
A bare metal roof on a coop in WI would be a very bad idea. It transfers cold much more than wood does, it gets condensation in the coop, it's really noisy in wind, rain, or when something like a branch falls on it.
Not sure what you mean by "very good insulation" because Woods Open Air coops aren't normally insulated. I have a Woods coop. Mine has OSB, covered by rubber roofing material, covered by metal roof.