Applying via the Italian Consulate in Melbourne or Sydney is the simplest and least expensive option to have your citizenship recognised (assuming you qualify). You can apply as an individual, or as a family group for multiple people residing at the same address.
Based on research done by a genealogist in 2018, it is impossible to get a bonafide birth certificate for Giuseppe Santamaria from Italy. This is due to the records from 1886 having been destroyed.
Not all hope is lost though - the municipality can issue a formal certification stating that “Giuseppe Santamaria was born in the Municipality of Leni, he was found inside the pandettes, but due to the destruction of birth records, it is not possible to fill in the certificate”. This official statement may be enough for the consulate to accept the jure sanguinis application.
Here is the genealogists explanation of the situation:
As for the birth certificate of Giuseppe Santamaria there is some problem. The registrer has been destroyed, and the copy of the register that is in Messina can not be used for a copy useful to the request of citizenship. However, a search was made at the “pandettes”. The pandettes are small registers containing annotations. Giuseppe Santamaria was found inside the pandettes, but it is not possible to write a birth certificate through the pandettes. However, the municipality can fill out a formal certification stating that “Giuseppe Santamaria was born in the Municipality of Leni, he was found inside the pandettes, but due to the destruction of birth records, it is not possible to fill in the certificate” . That is: Giuseppe was born in Leni, but we can not fill out the certificate.
This formal certification could help a lot in the request of citizenship, and in any case would represent a chance of success. It is not the first time that my clients use this certification in the process of citizenship, it is I usually send it.