Just shoot the darn things, Ed. I am sorry for the damage. As you know, I have struggled with the same problems, mink vs. chickens is not a fair fight.
Shotguns are good for lots of things, and minks are one of them. Winter holidays mean 2 weeks of free time for the boy. Buy his a box of ammo, make him stay up at night, and spotlight-em. Those big eyes glow in the dark, I assure you.