I'm interested in composting the run, but NOT interested in composting anything next to wood. When I garden the wood used for my raised beds rots out every 5 years.
I just bought my coop and I have figured out what to close and what to remain open to keep it dry and warm for my birds. ANY composting creates heat. I have a wooden floor and wooden walls. I have put vinyl on my floor to make it easier to clean up. I am sure that many chicken owners who have built a coop and left a dirt floor could experiment with this.
ANY method requires maintenance. I am satisfied to clean up after my birds inside of their coop, just as I clean up after my horses in their stalls.
Do as you wish. I cannot afford to buy a new coop in 5 years. THIS one was close to $1K.
MY point was that you have to clean up after your animals.
Perhaps I may try composting in the run.
I have a portable chicken tractor, bought my McMurray, that will need bricks to keep down, and I intend to let my hens clean up areas while I monitor and garden closeby.