In the link that I sent you:
All kinds of fowls. Coccidia itself is species specific.
So what affects your turkeys may not affect your other birds. When you say that the skin is darkening, are you talking about on the head or on the body? I have seen some articles that say that sometimes the skin on the head darkens, and others say that the head doesn't turn black and that it's unknown where the common name of blackhead comes from. I have no experience with it, so I don't know. Pretty much anything affecting the liver will give you that color poop, and the rest of the symptoms (droopiness, lethargic, etc...) is about the same for every illness that they get. When a turkey gets sick, they droop, have ruffled feathers, and huddle.
I am not saying that what you have is not blackhead, just saying that it could be something else. Is there anyone who could open one for you and you could post pics?
Do you have earthworms there? Just wondering because you mentioned a storm, and here when it rains the worms come out. There are a few diseases that earthworms can carry. Some folks spread lime where they keep the turkeys, I think it keeps the worms away or something?
I am really sorry about your little ones!