They would make good mulch for plant beds in any case.
I think I'd start with using them in the run, rather than the coop, where I assume it is already dry. (I use Stall Dry in my raised coop, which I really like in our weather).
Here are some pics of my wood mulch:
In the 'back up' pile, not used yet (leaves fell on the pile over Fall):
My Turken is modeling the mulch in the open run (dirtier and wetter, but the mulch stays above the mud):
What is this Stall Dry product you speak of? It sounds interesting, I'll have to do some research.
I like your run a lot, the floor looks a LOT nicer than the current state of ours. I'll see if I can snap some pics of it today. The mud is.. well, insane. In the "run" (free range area) the mud is 6+ inches thick in some places.
In the coop, one end is particularly muddy, while the other end is dry for dust baths. Further away on the property a literal pond has formed. It seems like this property is low and water is draining here, even though there is a french drain (big trench) halfway through it. Now that we know how bad the water gathers here, we have to do more trenching, but we need to wait for the dry season to do that.