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You state that your mother believes that your grandfather was Jewish, but you do not state why she has this belief. What is her evidence?
All the information you present seems to prove that your grandfather was not Jewish, but gentile. First, his name. As the name of saint, Stefan was rare, if not unknown, among Polish Jews. Although Polish civil records show Jews named Bulkon or Bulkin, there are none named Balkun. Yad Vashem, the Holocaust memorial and study center in Israel, on its web site shows four entries for Jews named Balkun, but all were natives of Romania. The passenger list of the SS Bulgaria shows that Stefan identified himself as Russian by ethnicity. Column 9 of the passenger list is headed "Race or People" and if you look through other pages of the manifest, you will see passengers identified as "Hebrew." If Stefan was Jewish, why did he not identify as such?
You mention "'russification' policies in the Russian Empire" that may have caused Stefan and his brother to join the Russian Orthodox Church in Scranton, Pennsylvania. Although there were Jews who converted to Christianity, there were no large-scale efforts in Tsarist Russia that converted Jews. If there were, then once Stefan and his brother were out of Russia they would have been free to identify as Jews. Yet, all of your evidence shows that they freely identified as Christian. You also state that several of Stefan's pall bearers seem to have Jewish names. What are the names that seem Jewish? I assume that Stefan had a church funeral. It would have been extremely unusual for Jews to have participated -- or been allowed to participate -- as pall bearers in a Russian Orthodox funeral.
Do you have any specific evidence that Stefan was Jewish? If not, you must assume that he was a Russian gentile.