You're welcome mfulayter
As to pronouncation try http://ivona.com
to translit your surname into Cyrillichttp://ua.translit.cc/
the KOZSU...would be Hungarian spelling. Your ancestors were Ruthenian.
If the church records are not showing up in LDS-Mormons than you most likely need to hire a research in Ukraine. I saw that you posted on Ukraine's Genforum so hoping that Hania will come and provide that information to you.
Thank you for locating Istvan's manifest. That is the same way you need to find Janos's.
Kazsukan, Janos Galocs, Hungary 16 1891 1907
Kozsuka, Janos Galocz 45 1859 1904
KOZSUKAN, Istvan, Magyar, Galocz; uncle LEGEZA Peter Tomkins Cove, NJ
arr. NY EI:
Legeza, Gyula Galois, Hungary 13 1900 1913 view view view view view
Legeza, Gyula Galos, Hungary 10 1900 1910
Legeza, Janos Galos, Hungary 52 1858 1910 view view view view view
Legeza, Janos Galoes 16 1890 1906
Legeza, Julia Galois, Hungary 48 1865 1913 view view view view view
Legeza, Julia Galois, Hungary 32 1881 1913 view view view view view
Legeza, Julia Galos, Hungary 48 1862 1910
Legeza, Sandor Galos, Hungary 12 1898 1910