Hi, Zlatica, thank you for your response and informative links.
No I haven't found my John Andrew (O)Brosky's manifest. He was called Andrew and he shortened his surname, and I can't find what the original would have been. All searches show nothing that I can match to him or his wife Josephine Zofia (Sophia) Gacek. Those you listed I also found, but they do not match her information beyond her immigration date. The 1920 & 1930 list it as 1898 & 1899 with a 1910 Naturalization. She would have gotten that as a derivative of John Andrew. Although the census records claim they came from Hungary, Austria, Andrew wrote on his daughter's 1914 death certificate, they came from Galicia.
Even though they both came from the same area, an older relative claims an unwed Sophie immigrated with her younger sister. Thus they would have married in America. Either in the Trenton, New Jersey, or Fayette, Pennsylvania, areas. However I can find nothing on them in those areas, and since I can't find their older children's birth certificate there—even though their death certificates and other documents claim those areas—I can only think they were registered under the original surname.
I have contacted their Catholic church—listed on a child's baptismal record—they refuse to answer. I have no idea why they don't respond.
I did find your Polish linguistics Web site helpful. I could see why they added the "sky" ending to their surname. I also discovered that Jan just means "son of" so that told me the "Ja?brocki" written on the child's baptismal record probably only meant Andrew had already begun changing his surname. We had thought it was the original surname, and we need only figure out what the unreadable letter was. Now we know the odds are that was just a version of the changed surname, so we have no clue what the full original version was.Albeit, thankyou for that Web link, it was very helpful.
I also tried looking for documents under your suggested "Broniszewski", but didn't find anything that matched.