Arborist wood chips are often free. Wood chips have a 500/1 carbon ratio that absorbs the manure and water from the run. Sprinkle azomite (stall refresher) to prevent the smell, if necessary.
My favorite way to get rid of mud is by adding a 6” layer of wood chips, they break down, but keep the mud away. Wait until you don’t see wood chips to shovel it out and you will find beautiful compost.