Neck area attacks can be an indication of weasels, ermine, mink or generally the Mustela genus. They often kill entire flocks, the initial birds for nutrition, the remaining for sport. Quite vicious. One cannot be certain without visually seeing them, as noted before it could be a animal...
I second the vetiricine. It's proven effective for us many times. Were most of the injuries in the same area of the birds like above? I'm so sorry for your loss.