I have a question for you... Where do you feed them? Is Layer feed around the corner? I have found that the worst run smell is not from poo, it's from wet wasted layer feed. I've had to solve for that and smell gone.... That said my soil is mostly sand and I have a layer of playchips on top, I just add to it every spring. Your run doesn't look like it would smell of poo to me if you're letting them out all day but I do understand issues with wetness, I'm in super rainy woods of Oregon.
I have a shelter for my feeder/waterer in my run: https://www.backyardchickens.com/articles/an-outdoor-shelter-for-the-feeder-and-waterer.76487/
My traditional, metal feeder has nearly-zero waste due to it's deep pan and inward-rolled rim.