I agree.....you'll need to go much deeper in a coop with a wood floor and you'll also want to be adding some moisture if you aren't able to generate enough with the amount of fecal matter and rotting litter. I am very blessed in that I am on a soil floor and have a very~intentionally~leaky coop that deposits water right where I need it when it rains or snow melts. The ground also contributes to my moisture as my coop sits at the base of a hill/slope.
Also, if you are currently stirring it up all the time, I'd cease and desist. Just flip the poop over or flip dry bedding over the poop, but don't try to stir the bedding. You have enough differences in particle size to create air pockets in your litter, so just flipping it lightly to keep the manure under the top of the bedding should suffice.
Keep heavier, more absorbent material at the bottom, such as the hay, and the lighter stuff added to the top, such as the leaves. I found a couple of bags of sawdust worked well beneath my roosts as the initial layer of DL and it really acted like a sponge for moisture and was so heavy with that, that the leaves and such just kind of rode on top of it. The chickens scratch there but they never get down deep enough to hit that sawdust~now compost~layer.
Another thing you might consider if your DL is always dry, is to add things that are moist....hay is good(not too much at any one time), grass clippings, garden refuse, kitchen scraps that are nice and wet, etc. You'll want to concentrate these things at or very near the area under your roosts for maximum effect...that's where most of the composting occurs while the rest of the bedding can be used to flip over manure under the roosts each day to trap their moisture and such under the top layer.