Hi, Danson. So sorry for your loss, but so happy that Sophia is in perfect health.
I do think that the only way you'd be able to determine Princess's cause of death for sure would be to have a necropsy (autopsy) done.
There are conditions that cause the symptoms you saw that can't be detected by xrays or even bloodwork. We had a setter, Evan, who came down with acute inflammatory bowel disease when he was 2. The onset was sudden and severe. He became lethargic, stopped eating, developed severe diarrhea and had tarry black stools. We were lucky enough to have a vet that referred us to the Veterinary Teaching Hospital 100 miles away and also fortunate that the VTH would take us immediately on an emergency basis. Had we not made the trip and gotten the diagnosis, Evan would not have made it through the weekend until the next regular appointment there. Had he gone untreated, he likely would have died within a week from the onset.
IBD does not show on xrays and unless you know what to look for, initially causes only subtle changes in bloodwork. The bloodwork shows the dehydration, but not much directly stemming from the IBD. And even as it was, jumping to diagnose the symptoms immediately and getting to VTH as fast as possible, it was still very touch-and-go after diagnosis before the treatments began to work.
I'm not saying that's what Princess had--what I'm saying is that it could have been any number of underlying causes other than a lodged chicken bone or distemper, and even if she'd been diagnosed for sure, she might still have died. It took 5 days for Evan's diagnosis to be made--and it took an intestinal punch biopsy to find the IBD. So there's probably nothing any vet could have done for you in one day to make her better.
I know how pinpointing a cause would be comforting, but likely you'll never know for sure.
I hope your happy memories of Princess eventually bring you comfort and some peace of mind. She was loved, and she knew it, and that was a wonderful gift to give her.