We are in Auburn.
In our smaller coop, we did the same thing, Sand and dirt floor and of course they always kick straw down there too, but it's no big deal. We don't use DE in the coop anymore, we just dust them. DE is too powdery and gets in my lungs as well as the chickens. We strive for as close to organic as we can, for the benefit of the eggs and the chickens.
Honestly, you should try a couple different things for a couple weeks to see what works best for your coop style. Some coops are all the way down to the ground and some set up off the ground. We used all kinds of different things in our first coop, which was off the ground. Cardboard, used feed sacks, straw, wood chips, etc. We experimented a bit to find what we liked best. In the end had our decision had more to do with the ease of cleaning and cost than anything. Since we have access to free grass clippings, free wood chips, free clean dirt and sand, we used those things.
Our flock free range during the day. They are pecking, laying, dusting and finding critters and bugs among all the things we used in the coop, and best of all, other than the straw, for softening up the nesting boxes, we are not putting out any money. At cleaning time, all those items can go directly into the compost, except the used feed sacks.
For those who are wondering, the white showing on the shelves in the coop are the used feed sacks laid out to catch the poo,.. not paper towels.... chicken poo is pretty heavy, I am not sure a paper towel would hold up. lol,, but good question.