Try the plywood and flour set up so you can get some tracks. Suggest you empty your coop, check for loose boards, roof steel, or holes gnawed thru the floor or a wall that your litter, nest boxes, or feeders are maybe camoflaging. Also if you can get in the coop, while it's empty, and close it up (make it dark inside) look for daylight coming in as a possible critter access. Watch the eaves and ventilation openings for wire pulled loose in a corner that moves but drops back into place when released. You may have a small critter attacking the birds and the rest of the flock is pecking at the carcass making the kill look like a larger animal. Reevaluate your wire, is it's openings big enough for a animal to reach and do damage from the outside?
Crawl the run wiring looking for gaps and look for broken wire and rusted wire. Is your skirting fully attached to the run wire?
Is the top wire fastened securly or is there gaps that allow the critter to push thru?
Suggest you try these ideas as well as evaluate if you need to elevate the coop as a animal may live underneath(no downstairs predator apartments). Good Luck with solving you critter problem