I liked your original idea of exclusion - we have just been through a weasel scare - see my photos in "Operation Weasel" under the predators topic - in your photo, on the left side, that looks like the hard wire cloth ends, though, does it?
I have hardwire cloth on floor, walls, and roof now - over coop windows, door, etc.
for floor see photos here:
https://www.backyardchickens.com/threads/operation-weasel-in-46-photos.1221150/
for walls and roof see photos here:
https://www.backyardchickens.com/threads/am-i-a-genius-or-an-idiot.1217242/page-5#post-19446930
no holes bigger than 1/4" - spied on my mice (who stink and bring other predators in behind them) and saw where they scurried when I shone a flashlight on them - then reinforced the tiniest holes with "great stuff" from Lowe's, an expandable foam that sealed spaces I could not get into with the wire - they can chew through that, but maybe it is harder than finding food elsewhere, I hope
Unfortunately, I have harmed many animals here through what I did or not did, but I would vote for compassion for all living things, including very smart, social, and sentient rats - we had rats as pets once - I adored them - I know it is not the same when they invade your home and coop, but remember that they are just like us, trying to live and eat and have a family and live where it is nice for them - I would take the niceness away and let them move on, if possible - total exclusion from food and shelter would be my response of choice, taking away the reason I created for them to be there, correcting my mistake without causing so much pain for them