First, I would move the birds into a garage, basement, something - secured and see if it still happens. In the meantime I would booby trap their usual coop/pen with poisons, game cam etc. Yes, you need strong hardware cloth everywhere there is fence, the openings are much too big in the wire you have now.
Is it possible acid could do the damage to them?? I haven't ruled out human predators at all. Is it possible something is coming up thru their feeder (rats??) and when they stick head in to eat it grabs them?? Like everyone else I am having nightmares over this - I know its a billion times worse for you. It's just so horrible and can't believe the victim could still move around and not be shrieking in pain.
I also would take a victim to the vet and see what he thinks about possible disease, fungus whatever. I'm sure he'd be interested enough to send samples maybe to the state etc. It is so horrific = I would think at least the county would get involved. Do you have chicken neighbors with anything like this going on???
I have subscribed to this link because I have to know what happened and how to stop it. My heart goes out to you and the poor helpless victims. Please, please let us know any further developments.
not sure why you seem to not believe it is a predator, your coop either way predator or not at this moment is not secure enough. a predator will come at some point and you may loose them all in one night. I hope you have secured that coop by now, we are the ones our chickens rely on to keep them safe and healthy. I would be doing eveything i could at this moment to protect those chickens, that is a horrible thing to have happen. good luck