I don't know about the wood shavings. I've mostly dealt with chickens where the litter was dry leaves, shredded newspaper, sometimes a bit of hay or straw, and similar things.One question, do you guys ever just throw poo filled shavings directly in a garden bed? I was thinking at the end of growing season just covering all the beds with uncomposted coop litter.
My mother would pile the chicken bedding (complete with lots of droppings) on the garden beds every spring and fall, and rototill it in. A few months later, it was all nicely broken down (as in, you could not longer find visible pieces of newspaper or hay or whatever.) That soil had lots of earthworms, too. I remember hauling the stuff, seeing her rototill, and planting seeds all on the same day-- but maybe not all in the same garden bed. She might have fertilized one bed, and planted seeds in a different one that day, and waited until later to plant in the one that just got manure. I never really understood her system, but I know she had it planned out somehow.
I'm pretty sure that tilling it into the soil helped it break down faster, both from being mixed with the dirt (and bacteria and worms), and because the rototiller chopped everything up into small pieces (more surface area helps it decompose faster.)