Do you have a walk in style chicken run? If so, I suggest that you put your coop bedding right into the run. Add the rest of your yard debris, perhaps a few bales of hay, and any materials from your kitchen that the chickens might eat. I'd not put out any dairy or meat unless they consume all of it. But if you have vegetable matter, toss that into the run. The chickens will eat what they want and the rest will be scratched into the deep litter. Your goal will be to make the deep litter at least 6" deep in the run. The chickens will take care of the composting process for you. The DL will attract all sorts of beneficial organisms which will help with the composting, provide beneficial bacteria and fungi to improve the immunity and digestion in your chicken's guts.
It takes a very long time for shavings to break down. The process will speed up in the run. But, b/c of the long break down time, and my gardening goals, I only buy shavings if I'm brooding chicks. I use lawn clippings and dry leaves as bedding in my coop. The bedding in the coop is DL also. When I do a partial clean out, I simply scoop the bedding into the run where the birds complete the composting process for me.