For once, internet discussion boards trump the experts.
The coop is located a mere 10-15 feet from my large kitchen window, which is always open. There is a low-grade but persistent odor that hangs around no matter how much I attempt to clean (and to be perfectly honest, I'm not so on top of the cleaning mostly). The only thing that has helped has been deep bedding in the pen, which makes a mess and prompts the girls to lay their eggs UNDER the coop. At first I thought that strategy was pretty daft, until I realized that I am the primary predator of their eggs, and that's the hardest place for me to reach them. Score one for the chickens.
If you check the multitude of chicken keeping handbooks and guides, everyone just says if you keep it clean enough, there won't be a smell. Well, shucks. I chalk this up to backyard chicken "experts" being more concerned with gaining converts than with solving practical problems. They don't smell! They're easy to care for! They're not noisy! (I believe we have discussed that last point before)
Maybe all that is true if you live on an acre and houses are spread out. But we're tightly packed here, so there is a low, low, low threshold for unacceptable odors and noise. Just sayin'.
Here's the other thing: for most of the year, it's pretty damp here. It's humid. The soil is clay and drains poorly. And keeping chickens un-smelly largely depends on a dry environment. They usually wind up walking around in a pen of wet clay, which is basically wet chicken poop. No amount of cleaning will correct that (they have a wire bottom cage, by the way, so most of their waste drops to the ground below).
Exasperated, I hit the discussion boards, and guess what, smelly pens are a common problem! Most people complain about it in the summer months, which is basically year round here. The most reasonable solution seemed to be applying a layer of lime to the ground, to neutralize the urea. After confirming my hydrated garden lime in the garage was too caustic, I found a 60lb bag of agricultural "Ag lime" at the garden center. I hauled it home and sprinkled a light dusting - like a nice light coating of new snow - to all the bare earth. I also sprinkled in the dog run, for good measure.
This is what I can tell you: two days later, and I can't detect ANY smell, even standing next to the pen. Also, despite trying to eat it, the hens are not dead.
Score one for me.