These are the symptoms of Newcastles-does any of this sound familiar?
I realize this is strictly an avian disease, but could this be what is killing your birds?
I know it sounds far fetched, but your situation is so odd, I looked up some odd things.
From Wikipedia:
"Signs of infection with NDV vary greatly depending on factors such as the strain of virus and the health, age and species of the host.
The incubation period for the disease ranges from 2 to 15 days. An infected bird may exhibit the following signs:
They can include respiratory signs (gasping, coughing), nervous signs (depression, inappetence, muscular tremors, drooping wings, twisting of head and neck, circling, complete paralysis), swelling of the tissues around the eyes and neck, greenish, watery diarrhoea, misshapen, rough- or thin-shelled eggs and reduced egg production.
In acute cases, the death is very sudden, and, in the beginning of the outbreak, the remaining birds do not seem to be sick. In flock with good immunity, however, the signs (respiratory an digestive) are mild and progressive, and are followed after 7 days by nervous symptoms, especially twisted heads."
A necropsy will show what is killing your flock- I would contact the State Dept. of Agriculture regardless-if there is some kind of epidemic going on, they need to be notified.
This really doesn't sound like coccidiosis to me, I could be wrong, though.
Good luck and make sure you and your family WASH YOUR HANDS, shoes, clothes, whatever has possibly come into contact with these animals.