But the problem isn't the wood. The problem is the feed and limiting the feed to one pm just means the rats are going to eat during the day.
Rodents almost always live within a few feet of their food source and the smaller the rodent the closer they tend to have very small territories they live in. Mice, ten to twelve feet from shelter to their food source, rats maybe double that. Why? Predators will get them if they venture out in the open and they leave urine trails that some predators can see due to the ability to see in more spectrums of light. Rats can and will tunnel under the coop if they don't have a handy wood pile, even there the wood pile is to shelter the tunnel entrance, they aren't living between the wood itself.
So unless your wood pile is right next to the coop it probably isn't contributing to the problem. Control the food, control the rodents.