I'm not a Schneible descendant, but am tracing the Heitz family for a friend.
Elias Steimer (1806-1872) of Ottenau and Rome NY was a first cousin of brothers Joseph and Gregor Heitz of those places. The other families from Ottenau in Rome might have been only former neighbors, but it's not unlikely that there was some blood connection between them. I believe I noticed the name Merkel showing up in both the Heitz and Schneible family trees.
The submission below at Ancestry.com takes Paul's line back a few generations. http://trees.ancestry.com/tree/13789209/family?cfpid=1286954...
Do a google search for "Paul Schneible" "Rome", using the quotation marks just like that. You might get some interesting hits like this, which you may already have:
MATTHEW SCHNEIBLE died at his home at Coonrod NY on Sunday (March 4, 1888). Dropsy was the cause. Mr. Schneible had been a resident of this country for 30 years. He was born in Germany. His wife and four sons, Valentine and Michael of New London, and Endock* and Paul of Rome. Deceased was a brother of Michael and Paul Schneible of this city.
*Endock should more than likely be Jodock Schneible (1847-1919). The baptismal records of St. Jodock's Catholic Church in Ottenau show several boys were given this delightful first name.
An article in the "Rome Citizen" of Aug. 8, 1899, says "Franz Schneible has gone to his old home in Ottenau, Germany". One Franz Schneible from Ottenau (no other identifying information) emigrated to North America in 1872.
Ancestry.com passport applications show a William Schneible of Philadelphia PA, b Ottenau 6 Nov 1859, applied in 1912. He had immigrated in 1884.