Thinking about deep litter method...

I have an approx. 10x12 coop that I currently use sand in. That's working ok (but I don't think I have enough sand in there). The run is about 10x25-ish and is barren dirt. I throw a chunk or two of straw in there every once in a while, but it's just breaks up over the next week or so and kind of absorbs into the soil. I just watched a video last night about someone that does the deep litter method with straw out in their run. They dig under the top layer of straw and exposed blacker-than-black compost. I'm thinking about doing that for my run. I have about 10 straw bales that have just been sitting outside for a year or so and aren't much good for anything else.

Any suggestions?

BTW, I plan to let my flock free-range again, but they're just coming of laying age, and I want them to realize where to lay their eggs before I let them out to lay them in the woods somewhere and they get used to that.

Also, my run has no roof on it yet, but that's happening very soon. The current fence is about 8ft high, and only my leghorn knows how to get out. Haha. Anyways, it will be enclosed within the next week or two, so they will probably just spend all winter in the run and not free ranging.