Is her crop emptying overnight?
I had a hen that began crowing, she laid eggs intermittently, but some were soft shelled. I did notice she seemed to crow more when her crop was slow to empty - not sure why but found it interesting. She lived about a year or so after she started crowing. She did develop a very full abdomen as well. When she died I performed a necropsy and saw what I think was cancer of the reproductive system so I just made the assumption the crowing could have been related to hormone imbalance from that.
Not saying your hen has cancer - but possible some type of hormone imbalance is causing the crowing.