A few follow ups, corrections and comments about my post and the replies I received here and privately.
I didn't provide as much detail as some asked or expected. I didn't imagine that others would try to research my family for me. Also, I wrote the note on my phone and tried to same myself typing more than absolutely necessary. I have reasonably good records of some key highlights of my family history once they arrive in the US. But only sketchy information about life in the Pale and immigration. I do have the yizkor book for Suchowola which features a passage (with a photo) about my great-great-grandparents Leyzer and Freydl Jaffe, and a long obituary of Henry's brother Zalman, who died in Tel Aviv, 1954. I have naturalization papers for Henry and individually for his sons Samuel and Albert, the manifest for Bessie, Samuel and Charles.
I have census records for the family starting 1900 with a farm in New Jersey (one of Baron de Hirsch's scheme). In the 1900 census, Bessie reported having 8 children, 8 living. Seven are recorded in the household in 1900. Elexander (Samuel), Charles, Jacob (born in Russian (Poland), Elizabeth (Memphis), Maurice and Freda (Phila.) and Solomon (NJ). Albert remained behind to finish rabbinic studies and immigrated in 1905, settling in Pittsburgh. I have various family entries from city directories, draft registrations. death certificates ... I'm in touch with Albert's granddaughter and Solomon's son. Henry, Bessie, Charles, Jacob and Elizabeth are buried in the family plot outside of Philadelphia (Mt. Sharon).
My ggf Henry didn't immigrate in 1875 as I wrote. (1875 was reported as his arrival date in the 1910 US census but 1887 arrival, reported elsewhere, is more likely.) He filed his intention to become a citizen in 1890 and I have what looks like the original Certificate of Naturalization filed in criminal court in Shelby County, Tennessee, 20 May 1895. Neither form provides information about his arrival. There is some family lore that Henry went back and forth, looking for a place to settle his family, apparently fathering some of the children during visits. I heard from a couple of sources that he and his brother Zalman went to Ottoman Palestine in the early 1880s. Henry left, either because of allergies or because he didn't like laws prohibiting Jews from owning land, but Zalman remained.
Henry apparently followed his younger brother Moses to Memphis when he arrives in 1887(-8). I have my ggm Bessie (Pesche) Steel Jaffe on a manifest traveling with two sons, Sender (Elexander or Samuel) and Gedale (Charles), arriving NY on the Red Sea from Bremen, 17 July 1893. I was able to line up Pesche, Sender and Gedale with Bessie, Samuel and Charles with the names on their gravestones, and the Last Residence entry on the manifest reads Suchowola, which we know to be their hometown.
Someone suggested I try to research and collate as much family data as possible to 1) look for other relatives who could have brought Jacob over with them and 2) establish as much data about Jacob to help search other arrival dates. To the first point, I can identify no other relatives on the Jaffe side who could have brought Jacob in time for him to be enumerated in the 1900 census. The only family remaining behind arrived in 1903 or later. The missing piece, which might provide an answer, is his mother Bessie's family. I barely know her parents' names (from her death certificate) and know nothing of siblings or other relations. Once I accept that Bessie came with two of her sons but left the youngest behind, the most likely scenario was that he arrived with other family, but I haven't found a record showing when or how this happened. For the second case, I have a spreadsheet with every data point I've encountered. Jacob reports immigrating 1892 (1910 census), 1893 (1900 census), 1897 (1920 census), 1899 (1930 census) and naturalized 1892 (1920 census), arrived 1893 and father naturalized 1895 (on Jacob's passport application). His year of birth varies from 1884 to 1888 depending when you asked.
Finally, at least two of you suggested using the searches available at https://stevemorse.org/ I've looked at this site but haven't discovered anything I wasn't able to find using the Ellis Island manifest search. Specifically, someone suggested searching simply by the Residence name but no service I've tried allows me to search without entering a family name. If there is a search tool that allows a broader approach, please provide a name or other pointers, Thanks.
p.s. For those who might be interested, the story my grandfather told me (and I recorded) is that he made the crossing at the age of 13, accompanying a younger cousin. They were smuggled across the Russian border and put on a train to Antwerp. The train was delayed and they arrived too late for the boat, requiring them to wait a week for the next ship. Since he was at leisure, my grandfather decided to explore the city. While in a public park surrounded by nice houses, a well-dressed man approached my grandfather and said to him, in perfect Yiddish, "Would you do me a favor? I need you take something to one of the houses here. Someone will give you an envelope in return. Bring it back to me. I'll be waiting for you." My grandfather said he knocked on the door and a woman answered, holding an envelope as if she expected him. He gave her his package and took the envelope back to where the man was waiting. The man took a large denomination bill from the envelope and gave it to my grandfather and walked away. (When I asked my grandfather what he thought that was about, he just shrugged.) He continued his trip, arriving in NY, where the cousin's family received him, took him to the baths and gave him a set of "modern" clothes. On the way to the baths, a ruffian called my grandfather a "greenie" and they got in a fight ("I got the best of him, believe you me."). The next morning they put him on a train to Philadelphia, with a note instructing the conductor where he needed to get to. Arriving in Phila., the conductor handed him over to a policeman who escorted him to his father's address. At his father's home, they were told that everyone was at work and the policeman took him there. However the foreman had them locked in and only after negotiations, one of the brothers was allowed to leave to take Jake to the house.
There are so many holes in the story, I don't know where to begin. Maybe he was telling someone else's story. Maybe it came from a book or a movie.