In a book about victims of Soviet terror, WW2 era, there is a short entry with the name Z^upienis, Stanislovas son of Kazimieras, born 1917, lived in the town of Grinkiskis, in the Radviliskis district of Siauliai region. He had been released from a prison in the 1940's. This surname spelling seems close to what you had for the father of Anthony, and the town does match. I tried looking for the Zupienis name in the Lithuanian on-line phone directory, but did not find any listings.
When I looked at the Bremen passenger list to see what passengers came from Grinkiskis, I found Constantin Mesoka, 4/11/1907, going to Chicago via the port Baltimore MD, traveling with Iwan Ramanska. The Mesoka name is so close to Mostaka name you posted, and seeing as how the passenger is from the same homeown, it is worth mentioning.
I'm not related.