That's handy to know, that I can let it pile until spring. I thought I had to rake it out and start again to keep it ok but I only seemed to rake out the ok stuff - that fits with what you say about the bad stuff working its way downwards. Also I was always worrying about where the next batch of litter was coming from.
I tell everyone that I start off with maybe 2-3 inches of (paper shreds) coop litter in the fall, add a thin, fresh layer maybe every 2 weeks, and by springtime I have somewhere between 10 and 12 inches of coop litter to clean out. It never smells in my coop. The fresh litter seems to stay on top and the chicken poo, for the most part, works its way down to the lowest layers of coop litter.
The top layers of coop litter always smell fine, but when I get down to the bottom, then it's definitely time to put on a dust mask and put up with some smell at the bottom. But, that's OK. All that used coop litter is great for the chicken run compost.
One problem I have sometimes in winter, is that the groundwater level rises and the soil becomes damp even without being rained on. If I can let the litter get deeper then it'll be easier to maintain the top layers nice and dry.
I would think that if you had your run litter high enough, the top layers would be pretty much dry while the lower layers would be soaking up the water and starting to compost. That is what goes on in my chicken run composting system, and it works just fine. The chickens pretty much maintain the top layers of the run litter with their constant scratching and pecking for food. Lots of worms and bugs in an aged chicken run compost litter system.
I do grow veg and the run litter seemed to do a lot of good last year, when made with shredded twigs and leaves, so it's good to know that paper will do the same.
Mine get scratch mix in the afternoon and they love to scratch more than anything else.
Paper sheds are a great source of carbon material, and they will compost faster than twigs and leaves. During the summer, I dump all my grass clippings in the run for the nitrogen and the chickens naturally mix the run litter while they scratch and peck for food. When I toss in my daily chicken scratch, I try to toss it on a new spot each day, which give the chickens even more incentive to work that area.
Because of aerial predator concerns, I don't let my chickens free range. But they seem plenty happy scratching and pecking in the chicken run compost system as I bring the free range to them in the form of wood chips, grass clippings, leaves, and just about anything else organic from yard cleanup. They don't eat the litter, of course, but the juicy bugs and worms that live in the litter must be good to eat. It seems to be a healthy ecosystem with lots of life in it.