Maybe you can get this shipped to you. Here is something similar to what I have used. The larger the bark pieces the better. You could at least build them an area in front of the coop to stay clean.
https://www.homedepot.com/p/Gardeners-2-cu-ft-Decorative-Bark-Large-8052/100290010
How big were the wood chips you tried? I get extra large bark style wood chips. You might be able to put enough of those down to get them out off the mud. How deep is the mud at this point? It might take quite a few bags. If it worked I would try not to walk in the run and your weight would...