So DLM (deep litter method) usually works better when your coop is open to the ground. That allows moisture, critters & microbes to work to break the litter & poops down. Also, unless you use wood chips, I've found a mix of materials to work best, not just one. Different sizes allows moisture to be contained in bottom layers and air to filter. Yes, it can be done in a coop such as yours. Introduce a couple of shovel fulls of "active" dirt from your garden, yard or from under some leafy shrubs/trees. It does need to have a little bit of moisture & since you've already protected your coop from moisture & molded, it could work. If its too wet or smelly, add more material. If it's gets too deep or you need compost, remove part of the material. Replace what you remove. Not removing all of it leaves a "culture" to keep the cold composting going. Most use this system in their runs & a deep bedding or other system in their coop.
It sounds like your coop is set up as a deep litter bedding system. The bedding/litter is only one material and should be kept dry. This will allow poop to dry out & somewhat break down, but it does not compost. If it gets wet, you would either remove wet bedding or stir it up as described by another poster. If gets stinky or you want it to "look cleaner", add more bedding. When too deep, you remove part or all bedding material & start over.
To get your hens to stir up your bedding - try giving some treats they like. Scratch or even pelleted feed flung into the area you want "worked", works. Or meal worms. If you use fruit, make sure to only use very small amount, making sure they find it all. Otherwise, in a deep bedding system, it can draw flies or create wet spots. That will make "scratching" (stirring the bedding) more attractive to the hens. You may have to try different times, to see when using the treats is best. Usually, they aren't going to scratch around bedding at night, so ...
