I'm a rank newbie and have no chickens at the moment, but from what you've said and from many accounts that I've read I'd think that it is coons. But, realistically, if you prevent coons from entering you will most likely prevent possums, foxes, and other small/medium sized predators from getting into the chicken proper, also.
Years ago I ran up on a really large possum in my open-ended garage. I had no chickens and wasn't really concerned about the possum being there. There was a vent-hood for a hotwater heater laying beside the wall from a recent project. As the possum sulked around the edge of the wall trying to avoid me and exit the garage it encountered this hood. The hole in the hood was something like 3-4 inches in diameter...the possum was big,..easily 10-12 inches (or more) in diameter through the body. When the possum encountered the hood, rather than going around it or over it it decided to go through the hole. I panicked in thinking that I was about to have a live possum hung up in that hood inside my garage...oh boy. Well, the possum entered the hole in that hood and is was like it was a fluid that just flowed through the hole...water wouldn't have flowed any easier through the hole!!! I was stunned by the ease by which that possum passed through a hole that was much, much smaller that it was. That big possum could have easily fit through a hole a good bit smaller than that vent hood.
Having witnessed that possum slide through that vent hood with such ease makes me wonder about 2x4 welded wire...with a strand of wire bent to one side from a lawnmower bumping it, installation bump, or whatever, it seems a 2" wide mesh could easily be changed into a 2-1/2" to 3" wide mesh which a possum could pass through easily. Fence/perimeter inspections should be a routine, I would think.
Can a raccoon and a possum that are the same size pass through the same size holes?
Ed