Schultz Family of Syracuse NY from Warsaw Poland

My maternal Great Grandfather, Henry S Schultz (July, 1891) , came to NY at 19 years old (1910), from Warsaw, Poland, which at the time was part of the Russian Empire. He married Frances Mandel and settled in Syracuse. Henry and Francis had 5 children, Helen, Arthur, Henry, Donald and Anna. My Grandfather, Henry Stanley Schultz, Jr. married Charlotte Roberts of Newark Valley, NY and had 2 children, Ronald and my mother Diane Schultz Meyers.
I am writing because I've reached an absolute dead end on my Great Grandfather's Polish lineage. He never spoke of his time in Poland, at least to surviving family members and his parents names aren't listed on any known US documents. I've researched the Ellis Island Immigration Records and Ship Records, to no avail.
I was told he came in on the Hamburg (alone) to NY City in 1910. I don't have a date of arrival. He became naturalized in 1925. He more than likely changed his surname when he landed in the US, but I am unsure. He was a practicing Roman Catholic for his entire life here in Syracuse and it's my understanding that he was in the Roman Catholic Church in Poland also.
I am looking for any possible family that may have come to the US before or after 1910 and had a relative from Warsaw, Poland that was born on June 26, 1891 from a family with a name variation of Schultz, or first name Henry? Possibly Heinrich or something similar?
Hope I have found the right person to give this too it came to me by mistake.
Subject: HENRY S SCHULTZ
To: family001
From: edmondsallan
Date: 2013-07-28 18:34:34
Hi, this looks to be him with wife and his family - regards edmondsallan - IQG
Henry S Schultz in household of Henry Schultz, "United States Census, 1930"
Name: Henry S Schultz
Titles and Terms:
Event Type: Census
Event Year: 1930
Event Place: Syracuse, Onondaga, New York, United States
District: 0020
Gender: Male
Age: 12
Marital Status: Single
Race: White
Race (Original): White
Relationship to Head of Household: Son
Relationship to Head of Household (Original): Son
Birth Year (Estimated): 1918
Birthplace: New York
Immigration Year:
Father's Birthplace: Poland
Mother's Birthplace: New York
Sheet Number and Letter: 7A
Household ID: 124
Line Number: 33
Affiliate Name: The U.S. National Archives and Records Administration (NARA)
Affiliate Publication Number: T626
Affiliate Film Number: 1626
GS Film number: 2341360
Digital Folder Number: 004639196
Image Number: 00189
Household Gender Age Birthplace
Head Henry Schultz M 39 Poland
Wife Francis E Schultz F 36 New York
Daughter Helen F Schultz F 16 New York
Daughter Anna H Schultz F 14 Pennsylvania
Son Henry S Schultz M 12 New York
Son Albert J Schultz M 10 New York
Son Donald E Schultz M 2 New York
Sources
Citing this Record
"United States Census, 1930," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/X4RV-RFM : accessed 28 Jul 2013), Henry S Schultz in entry for Henry Schultz, 1930.
Thank you for your response. I have all of the information I can get on my great grandfather through the census, ss death records, etc. What I cannot find are records of his parents, possible siblings before he came to US in 1910.