A word about the peat moss, the picture Miracle Grow brand the op has, says "enriched". I'm assuming they have fertilizer added, as they do to most of their products (even perlite). I wonder if that could cause a problem if the chickens eat any of the peat moss.
All the other brands seem to be plain peat moss. I hybridize house plants(streptocarpus), pasteurize peat moss and make up my own soil mixes so I check the labels before buying.