I do use the deep litter method! It works great. My coop floor is on the ground, and is about 6x8. I started things off with pine shavings, about 12-14" deep, and topped that with a square bale of hay, spread over the top of the shavings. I also put hay in the laying boxes. (For my open front laying boxes, pine shavings do not stay in the box. The hens build little nests from the hay, and seem to like it.) I have a small (5-tine) garden rake, which I use to occasionally rake the top of the hay around beneath the roosts. The coop stays very nice and dry. I have excellent ventilation, and leave the coop door open most days. In that space, 10 full grown chickens roost each night. The laying boxes stay nice, and occasionally need a handful of hay added to them. This setup has been used since March, without the need to add any more hay. My chickens free range during most days. Out in the pen/run is another story. They spend more active time in there, and the pair of ducks make a quackmire of it on a regular basis. But by adding additional hay every two-three weeks, I've been able to keep it livable, even with all the rain we've had. Before adding the two ducks, it was actually very clean and dry in the pen. After a big recent rain, I did remove some of the hay from the pen, as the ducks had sufficiently nastied it to the point that the deep litter was trapping or damming water that was running down the hill toward the pen. After removing some of the worst of it, I used a couple square bales to put on the floor, and I was good to go again. For reference, the pen is made from a 15' round trampoline, put up off the ground about 7 feet, on metal pvc pipes, then tightly covered top to bottom in hardwire cloth. So, the pen is about 177 square feet.
And like I mentioned, most days they all free range.
I plan to build the ducks a separate enclose soon. They never go in the coop, and that makes all the difference in there.
So, I HIGHLY RECOMMEND the deep litter method, even here, and maybe especially here, in the muggy Ouachita area.