I've watched most of Shawn Woods videos. He is a heck of a skilled craftsman as well as an interesting youtuber.
Here's the best trap I've seen him use for rats. It's just a bunch of old school spring rat traps (which I read are hard for you to set, but there are modern traps that are easier to set and I'm sure could be used in place of these.). This method prevents the rat from coming in from some weird angle and pretty much guarantees a snapped neck.
To keep the chickens from sticking their heads in, another box could be used and placed on top of it with a hole in it big enough for a rat, but too small for a chicken.
To hear Shawn say this is his best trapping system is pretty much a guarantee to be the best system.
Like Jay said, and like he mentions in the video, bait the traps for a while but don't set them. Let the rats get used to the setup, and then load it up.
Or, if you want to go totally natural route (and I'm going to say this is about the most permie possible way to catch rats), call this guy! He TRAINS! mink from fur farms to hunt side by side with his dogs to hunt rats and chase them out of holes. It's quite entertaining. I heard Shawn say sometime he might collaborate with Joseph (the Mink Man) and do some kind of hunting episode together.
Edit, I don't see why these easy to set traps couldn't be modified to work in the same system. https://www.amazon.com/Professional-Infestation-Solutions-AntiRodent-Protection/dp/B01MZ19B3O/ref=sr_1_6?dchild=1&keywords=easy+set+rat+trap&qid=1626726447&sr=8-6