One thing that I can think of is that we vertebrates, both humans and chickens, need an adequate amount of vitamin D in order for the body to actually absorb the calcium and put it to use.
I don't know if there are standards for vitamin D for chickens. I would think that it's added to commercial chicken feed in high enough quantities for chickens with normal metabolisms. But perhaps for chickens where something has gone awry, low vitamin D might be the culprit? Also, if they get out and about in the sunshine, their bodies will metabolize vitamin D from the sun. I know you've tried different calcium sources. Have you tried human calcium tablets, and if so, do they also have vitamin D?
What breeds are your girls, and how old are they? Sometimes with the chicken breeds created for high production and general commercial use, their bodies just can't keep up with the demand to create and lay daily extra-large eggs, and their reproductive systems become damaged.