I checked Genealogical Resources in the New York Metropolitan Area, edited by Estelle M. Guzik. It was published in 1989 and may be out-of-date in some respects. I heard that a later edition was issued. Page 272 says that the New Jersey State Library in Trenton has the 1895-1915 NJ State censuses; it says they are not indexed. Try to verify that fact on the Internet.
You may have heard that the Federal Census of 1890 was destroyed.
Guzik, p. 270 says that naturalization records are arranged by county and are indexed--perhaps by the first letter only of the surname. I call that rough alphabetization. Great-grandmother Paula had children born before her emigration, so they were aliens and may have sought citizenship.
In any case, the expertise you need might exist outside of the orphanage and adoption message boards. Ancestry.com has a board for genealogists concerned with Passaic County :http://boards.ancestry.com/mbexec?htx=board&r=an&p=l...
If that is not the relevant county, use the search box on the bottom of every page in Ancestry.com to enter the name of a county or state or surname for which you seek a board.
I used to read a message board for New York County, NY and many people had trouble determining the correct enumeration district in a federal or state census. For this reason, I suggest that one get help (free, if possible) from genealogists with experience in census research.
By the way, you use the name Paul(e/a) in your postings. A computer search for Paula on this message board will not find it, but her daughter's name Paula will be found. Some of the queries contain terms which frustrate computer searches, for example, a search for 1963 will not find 1962/63.