We have a similar size coop and we use a metal oil drip pan with granular PDZ sprinkled on top. We scrape it daily into our compost area. We ha e 7 hens and 2 roosts. Easy peasy to finish this daily chore.
Very nice, similar to ours, but we used white tarp to cover. We recently were having condinsation issue which we solved with 1/2" bubble wrap sandwiched between cattle panels and tarp. We do have a 4x6 coop attached, so this area is their covered run.