Thanks for the info but I'm still mystified. She was fine until she molted and has consistently had his issue since the molt. If you can get extra calcium down her the egg shells improve but she resists eating extra calcium. The other hens are OK. It sounds like she is not processing or eating enough calcium now but used to. I don't know why that changed.
The small bones will get ground up in her gizzard and be processed by her body. She will get some calcium out of them. Even when they eat oyster shell, egg shells, or other calcium sources not all the calcium is absorbed by a hen's body. A fair amount passes on through and out her rear end. Compost made with chicken manure is generally high in calcium, a good thing for gardens. I don't know how a chicken's body processes ground up bone compared to ground up oyster shell, I'd think pretty well.
Chicken Layer feed has about 4% calcium. If all they eat is Layer that should provide enough calcium for egg shells. So about 4% of what she eats should be calcium. I'm not sure you will feed her enough bones to get that, but she will get some calcium from other things she eats. It's not how much calcium is in one bite, it's how many total grams of calcium she eats in a day from all sources. So the bones should help.
Have you considered trying feeding her bone meal? I don't know if she will eat it or not. Like any "treat" I would not overdo it, but a little may help.
It may have something to do with Vitamin D. They get vitamin D from being outside in the sun or maybe from what they eat. The more vitamin D they have the more calcium they use from what they eat. Another way to say that is the more vitamin D they have the less calcium they need to eat or the less vitamin D they have the more calcium they need to eat. This is a bit of a slippery slope as these need to be in balance. Too much of both can lead to super-absorption of calcium which can lead to liver damage. There is a pretty wide window of what works but you might try feeding her extra vitamin D. I'm not sure of a good source for that.
When I have an issue I try to solve it for the benefit of the entire flock, not one individual. Since this individual appears to have special dietary needs I'd be reluctant to expose the rest of the flock to excess nutrients to benefit her. If you are willing to put in the effort you can try to find a solution to her issue but I'd be careful with the rest of the flock. I have been called ruthless because of the way I manage my flock as i have removed individuals that just did not fit in for behaviors or issues like this. Beyond a certain point, the effort isn't worth it to me. It may be to you.