Deterrents do not work and mothballs aren't legal in some states as they can leach into the ground, plus they also do not work. Hardware cloth, patching holes and reinforcing the perimeter are your best best. Make sure chicken feed is not inviting mice and rats into the area. Trap vermin rather than poisoning as they can track the poison into the coop.
Hawks, opossums, raccoons, dogs, cats--everybody likes chicken. But we're not willing to share.
It is impractical to cover every single inch of a large run with hardware cloth. We have covered every inch of our run with chicken wire. The attached coop has hardware cloth around the base. Snakes--as we all know--go right through chicken wire (as well as pretty much any small space they can find).
And since we keep about 2 dozen chickens, there is no doubt ample scent in the air for the snakes to zero in on. I too hate the idea of poison of any kind. Mice and rats are very common here where I live. The dogs like catching them. Oh--and bunnies, lots of wild bunnies. We're in the country, after all.
Bottom line for me anyway, is to keep seeking ways to safely trap without hurting my cats and dogs. I'm supposed to be smarter than the predators. So...game on!