I doubt if the broken egg she had recently caused the peritonitis. She probably had it for awhile. They can sometimes get an oviduct infection from bacteria entering upward from the vent. E.coli is an opportunistic bacteria , pretty much everywhere in coops, and sometimes other bacteria may be around. They can suffer with an oviduct infection and peritonitis for weeks or months. But this last episode probably just did her in.
Thank you for sharing the results, and glad that it was not something that would affect your others.