I have a few bits of info on the Concilla & Tardo families. The parents of Sam Concilla were Antonia [bn ca 1847 Italy] and Josephine [bn ca 1848 Italy]. This info can be found on the 1920 census for Sam Concella [note spelling]. Sam, a shoemaker who owned his own shop, had his parents and brother-in-law, Santo Tardo [bn ca 1908 LA] living with him and Vida [bn ca 1892 LA, IT, IT]. Sam, Vida and Joyce were listed on the 1930 and 1940 census records.
In 1900 I found the Tardo family living in Lafourche Parish:
Nick Tardo 1/1866 Italy
Annie 4/1879 Italy
Vitta 6/1894 LA
Congettina 12/1895 LA
Katherine 12/1899 LA
Dominick 10/1896 LA
Nick Tardo died 10/27/1948 in Lafourche Parish at age 84, bn ca 1864 Italy, his father is listed as Dominic.
There is a Dominick Tardo who died in Orleans Parish at age 68 on 4/20/1965. This may be the son of Nick and Annie. His obit is in the Times-Picayune - 5/21 page 2/col. 8.
Sam Cancilla immigrated in 1898, but I didn't find a definitive record. Nick Tardo immigrated in 1888 and I didn't find a record.
Mrs. Antonia Cancilla died 3/19/1938 at age 88 in Iberia Parish. This is surely Josephine. I did not find her and Antonia on the 1930 census and at least she was still living in 1930. I also did not find the Cancilla family in 1900 and 1910. They may not have been in LA yet, although they would have been in the country.
A John Tortorich died 1/1/1927 in Ville Platte. He was born ca 1878 in Tribia [Trabia], Italy. He may have been the father of the John who married Joyce.
In 1942 Sam Cancilla registered for the draft. His date of birth is shown as 12/12/1889. There is a Sam who died 1/1964. His SS# was 435-48-8370. The application for his SS would give valuable information. Or, a death record can be obtained at the State Archives for $5.00.
I hope that this info will be of use to you in your research.