If I remember right, she's an ex-batt like mine?
I had one of my hens lay soft shell eggs for a few periods, that once lasted up to a month. I also gave egg shells, oysters shells and liquid minerals but nothing helped. We ended up simply giving her a small "special" almost every day with a high protein content, either egg or sardine, mixed with semolina and lentil, and some vitamins mixed in, for support.
I think it's just that their reproductive system is screwed up.
However I don't understand how yours could be broody and laying soft shelled at the same time. If she is broody she shouldn't be laying. Maybe she's not being broody but just nesting for a very long time because she has trouble passing the egg?
Mine always pull out of it, but unfortunately it can also be something bad like ovarian cancer.