I am currently researching the Tuz family from the catholic church records of Jaryczow Nowy, Poland which is now the Ukraine. On 18 Feb 1838, Gregory Tuz, son of Andreas Tuz and Catherine Kuzmin, married Marianna Kaczorowska, daughter of Johannes Kaczorowski and Agnetiz Poszewska.
My great grandmother, Catherine Tuz, b 1840, is also in these church records but I have not confirmed yet if Gregory and Marianna are her parents.
People of this region are listed as Austrian, Galician, Ruthenian...
While these records are earlier than you are discussing, there may be a connection.
I am happy to keep you in mind as I continue my research!