You're correct. The cecal worm is host to the protozoa that causes Blackhead. The protozoa is deadly to turkey's, not so much in chickens. This is why chickens and turkey's should be kept at a distance from each other. They must be kept OFF THE SAME SOIL, penned a good distance away from each other and not allowed to free range together.
Safeguard liquid goat wormer or Valbazen will eliminate the cecal worms (carriers of the protozoa).
You will need to dose your chickens with Metronidazole to kill the protozoa. Then establish a monthly worming routine to eliminate the cecal worm lifecycle. Ending the cecal worms lifecycle will stop the protozoa from infecting your birds via cecal worms.