I am also the great grandson of Francesco Giardina born in 1887. But my Francesco was born in Pozzallo, Sicily and moved to Buffalo New York.
Here is the information I have:
Giovanni Giardina was born in the early 1800s and married Giuseppeina Armenia in the mid 1800's. Their kids are:
Then Giuseppe Giardina married Rafaela Salonia, and they had these kids:
Adelina 1906- ___
Francesco then moved to Buffalo, New York sometime in the early 1900s.