I think your 2nd great grandmother's 1st name was Gaetana, which was a common female name. If her last name was what it looks like, perhaps she was abandoned at birth (they were often given uncommon surnames) or was born in a neighboring town.
On my next trip to the FHC, I'm going to take a quick detour and try to find Maria Grazia and Agata's birth records. If the dates of birth are correct and they were born in Ausonia, I should be able to find them. Then we'll have the names of your 2nd great grandparents and I can look for their birth records. Unfortunately, Angela was born after 1900 and her birth record was probably not filmed.