I JUST ran into the exact same problem last month & they got into my screened porch & laundry room too!!!
I admit I did not read all 39 pages, I skimmed through to the end... but I didn't see this idea mentioned.
Have you tried DIY rat bait NOT poisonous to your animals? I don't use anything that would harm my pets if consumed (bait or dead rodent).
There are several variations of this, but eating baking soda will kill the rats & mice because they cannot burp or pass gas, but you must disguise the smell and add something to attract them!
Mix equal amount of:
Cornmeal (or Flour) and Baking soda, then add sugar & mix well. (ie: 1 cup Cornmeal & 1 cup baking soda with 1/2 cup sugar)
Add just enough water to make rather dry balls of the bait. Use gloves so your sent is hidden. Place the balls out of reach of chickens where the rodents would pass to get into your coop. Then they'll get thirsty & gas builds up... this should eliminate them over a week or two depending on how bad the infestation is.
You can look this up on YouTube too if you want a better idea.
I hope this helps... The rats made my dog sick, scared my chickens & stink! I was going crazy!