Good news! The girls are better and I didn't have to waste eggs or cull birds. Whew! After a long conversation with the NC Department of Agriculture poultry specialist, the expert my county extension agent recommended, I have a better understanding of what is going on and, best of all, a diagnosis. The birds have Chronic Respiratory Disease caused by mycoplasma gallisepticum, or "MG". It is common worldwide and poses no threat to humans that consume the eggs. Unfortunately, the chickens never fully eradicate the germ from their systems and can get sick again when stressed. Severe infections can kill a chicken, but since only a few of my girls got sick and everybody is still alive and kickin', our outbreak must have been mild.
For the technical information, visit here: http://www.ces.ncsu.edu/depts/poulsci/tech_manuals/mycoplasma_gallisepticum.pdf