That looks like a good idea. But would you specifically have to know what the wood chips were. The Power line trimmers are always willing to dump but they have all kinds of bushes and vines mixed in.
As Melky stated, there's some concern with using cedar. Opinions and experiences vary, minimal amounts possibly wouldn't be as harmful in an outdoor well ventilated area. My large maple tree was already being removed, so I just wanted to keep the free firewood and utilize the leftover chips.
I do not use deep litter as the more you leave wet litter in coop it raises ammonia levels and humidity which is not good for the birds. I just sift with kitty scoop manure from mulch/peat and replace mulch/peat in run as I send it over to my compost bins later to be placed in my gardens.
I've never had the litter get wet inside my coop. I stir it frequently and add fresh shavings to the top, the poo dries out quickly. I have a poop tray under the roosts filled with Sweet PDZ stall granules that gets scooped out like cat litter, maybe similar to your method. I love composting too! My gardens have grown better than ever these last few years.
Mind if I jump in on this thread? My girls free range so are able to keep out of the muddiest areas (and they seem to like perching on the kids' climbing frame!) but with the recent spate of wet weather, the actual run and the area around it are one big patch of mud, despite the run itself being covered with a tarp. Their food and water are inside the run and they have 24/7 access to it (I lock the run door at night but leave the pop-hole open for ventilation) so they do spend a bit of time in there. Is there anything I could/should be doing as a short-term measure while the weather is so wet?
Sounds like your run may not have the greatest drainage. Maybe the water is collecting from roof runoff and just seeping back under and into the run? That happened to me before. You could install a gutter, rain collection system, french drain or even a trench to redirect where the water flows.
Is it possible to move your coop to higher ground?
If you can't keep the water from entering, you could try to temporarily raise the floor somehow. I've heard of some people laying out pallets so the chickens' feet won't have direct contact with the ground, but you will still need to provide a dry dust bath area. It's really so much better to keep them in a dry environment but sometimes can be so difficult. Mud is a nasty beast to deal with, it was just so awful back when I had horses too. Seemed like no matter how much material I added and layered (wood chips, gravel, straw, anything!) it would just sink down and get covered again by more mud.
That's why I use that poultry net barrier method now, (along with my gutter system) it just keeps everything from sinking and drowning. And
@Folly's place has a point with landscape fabric as a barrier... with chickens, they just scratch it up and make giant fluffy chunks of it all over the place, exposing the mud once again!
If I've learned anything over the last few decades caring for animals, it's that not every method will work the same for every person or circumstance. Your best solution usually comes with trial and error. Good luck with your efforts!