Palmetto bugs? no, here in New Orleans we call them "Creole Butterflies" it just sounds nicer (tourist town you know= no bad roach talk.)
My family has been here in town from the 1720's and we do know a lot about these creatures. A great non-chemical way to get the population down ( ya ain't never gonna get rid of them) is to make "roach traps" and place them outdoors near your coop.
Items needed:
A large can, or gallon glass jar.
Shorting ( solid or spray type)
Sweet soda- any flavor
Spray or wipe the inside of your can or jar with the shorting then pour a inch or two of soda in the bottom. The "Creole Butterflies/Palmetto Bugs" will crawl in and drown
when they can't climb out.
Now for the icky part- don't empty the trap, the smell of the roaches will attract more and more to their deaths.
If it rains cover the trap, you will need to clean it out every week 1/2 or so, as you will have dozens and dozens of dead ones by then.
The traps will over time lower your yard infestations.
Good Luck