I've tried to address all these issues you have mentioned. The three hens came from the same breeder. I do not know if they are related. They do not look alike, so I would assume that if they are related it is not a strong relation (one hen is barred, one is all gray, and the other is more cinnamon). The rooster I have is from a different source so he is not related to the hens. The lady I bought them from had tried hatching eggs for months and only got 4 chicks to hatch (all cockerels). I was trying to see the glass as half full and assume she just didn't know how to run an incubator. LOL My hatch success has been just as poor as hers. I'm thinking it could be a genetic thing. I crossed my CCL rooster with some other hens and those eggs all hatched, so he is apparently capable of producing viable chicks. I incubated my CCL eggs along with other eggs from my flock both with broodies and in an incubator. The hatch rate was 85 - 100% for the non-legbar eggs, and 0% for the CCL eggs. They candle fine on day 7 and 10, and then die after that. The shells seem fine, it is just the yolk that is runny and the membranes seem weak.
My flock has a 200 SF coop, but they free range during the day and come in to roost at night. The CCL hens do not free range much. They will go about 30 feet in front of the barn, and that is it. They are the only ones near the coop all day and are often inside for a large portion of the day. They have all the food and water to themselves. On top of that they are fairly aggressive and will chase the other chickens if they feel like it. I have tried to give them extra vitamins, but they are not nice birds and don't like people. At least one of them bites, so you have to be sneaky when catching them. I've tried putting vitamins on bread...two of the hens eat it, but the third thinks I am poisoning them and won't touch it (that is the biting one, too).
Maybe I will try to get some Vitamin D into them. I'm starting to believe they come from a line of CCLs that have genetic problems. Our rooster has become really aggressive, so at this point I'm not sure how much longer we can keep him or where we'll go with the CCLs. They all just finished molting and should be laying again shortly. I would like to try to hatch one more batch of eggs. After that, the rooster will be gone. I might try to cross the hens with a Marans rooster to produce some sex-linked Olive Eggers. If those hatched it would show the hens aren't compatible with my current rooster. If that doesn't work, I suppose I will give them to my neighbor to use as laying hens. Unfortunately I would loose my initial investment in the birds, but perhaps that is better than continuing to invest money in them with no results.