As I waded through that thread, the thought that kept coming to me was "why not do both"?
When working with a compost pile, what quickly becomes evident is the more variety you can add to it, the better. Coarse (wood chips) and fine......straw......and chicken manure (nitrogen), as well as grass clippings and just about anything else you can throw in there will help. If it is wet or smells, add more chips and straw (carbon). Coarse enough some air can get to it........moist enough to support the bugs and get things breaking down. Not wet......moist. Big difference. Goal is to get the right proportions of carbon, nitrogen, air and water to make the compost pile work, and then keep it there.
And use the birds to mix it. Scratch grains are just that.......toss out a hand full or two on top of the litter and watch them go to work scratching and digging.......and in the process, working the compost pile......mixing and aerating. Get that right and it should not be wet or smelly......well not bad smelly. More like good smelly as good compost is.