Do you clean poop out of the coop in a separate manner? I have 9 chickens, and I can fill a 5 gallon bucket with poop from their poop board in about 2 weeks. Chickens poop A LOT. If all of their poop is going into the run, you might be surprised how much poop there actually is mixed into all that bedding you mentioned. If the majority of their poop (produced while roosting typically) is being removed and dealt with separately, then I would agree with your statements above that the run likely contains little poop in perspective to a 12-18 inches of bedding.
That said, all of our chicken poop from the poop boards go to a traditional compost pile. When I muck the run it too goes into a pile, although a bit less necessary.
There's also parasites and other nasties like harmful bacteria (E. Coli to name one) to consider. When applying run bedding directly to the garden as compost, these harmful organisms are distributed to your garden beds. Hot composting may help reduce or eliminate these harmful organism (there are of course various factors to consider, temperature of the pile being a key factor for sure). I imagine freezing winter temps may help eliminate some harmful organisms also, so perhaps it's not so bad to apply in late Fall or early Winter. I've honestly not done much research on that bit. My biggest concerns though would be E. Coli and various parasitic worms. If winter freeze takes care of these in the upper part of the soil, then I say your method is safe. That's an unknown factor for me though. Guess what I'll be googling later...
