Y'know, I don't even spread the new shavings - the chickens do that just fine by themselves!
I bring in a new bale and dump it in whichever part of the coop (17 X 22 former garage) seems to be the lowest. By the next morning, the flock has scratched it all out fairly evenly.
Fifty some chickens of all ages, from 10 week old chicks to the 2 year old dominant rooster, plus 6 adult ducks, 4 ducklings, and a pair of Toulouse geese manage to spread the pine shavings very well.
And I don't clean OUT the coop at all. I scrape off accumulated poop from the various non-floor places they've deposited it and either toss it into the shavings, kicking it around a bit, or I put it into a bucket and add it to the compost bin.