I appreciate the comment, but the "cooked chicken" was not what you'd call cheesy pus deposits, though there was a small amount of that in addition to the other stuff in the cyst. I've seen quite a few of those cheesy masses, having lost 15 or so hens to internal laying. I could show you a lot of pictures, having opened up hen after hen who died from it. She had never had egg issues and was a breeder quality hen, not immune, but certainly not the normal hatchery stock that almost every other hen was I've lost to EYP and/or internal laying. By the way, though I did not cut into her abdomen, I did peer up into it as far as I could from the hole in the back and saw nothing else out of the ordinary, only the weirdness inside the cyst.
So, no, this was not your normal thing. It was like the cysts where you find teeth and other bodily "things" inside in humans. I have one more hen with a similar cyst who is up in age and I may open that up as well when she passes, just to see if it was similar.
This is one of those "just when you think you've seen it all" things with chickens...