I wish to thank everyone for their replies so far (some also off list).
I have tried to reply to each person, personally. As a general follow up, first of all, the crop of ship manifest that I sent was from 1919 and not as I stated, and thank you to those who noticed and pointed this out and this changes the perspective a bit.
I was unable to find Sarah ZILINKOWSKY's grave on Billion Graves or Find-a-Grave - is there anyone, please, with additional search possibilities?
From the 1910 census that Michele quoted below, it seems that Simcha started using the name Simon ZAYON, and I found the grave stone of Simon D. ZAYON in Lakewood:- http://data.jewishgen.org/imagedata/jowbr/USA-00048/H3753.JPG
It mentions on his stone the names of the children. It seems that his wife was no longer alive, otherwise I am sure that she also would have also been mentioned. In any case, from this, his father's name was Elimelech - a name I am going to try and follow up on Eastern European archives through Jewishgen and JRI-Poland.
Ma'aleh Adumim, Israel