tracking a single female immigrant relative #usa

Rod MacNeil

I would be interested in hearing thoughts on tracing the life of a single female relative who emigrated to the United States from Horodenka (then Poland, now Ukraine) in 1920.
This relative's father, Hersch Melzer, had come earlier and sadly died very young within a few years (1906).  He is buried in Mt. Zion Cemetery in Queens, NY.
It appears that his wife (Feige Halpern) and their three children (Solomon, Leib and Jente) were preparing to come the US when news of his death cancelled their trip.
Their one daughter (Jente, age 17) came in the fall of 1920 with her single uncle on the same passage as his sister-in-law, my great-grandmother, Blima Hartenstein Halpern, and three of her children.  The uncle went to California after a few years and seems to have disappeared from the family's life.
I have the birth records of the parents and the children of the Melzer/Halpern family (Horodenka, then Galicia, Austria) as well as the manifest of the daughter.  I have searched the archives of this list to see how other woman with the name "Jente" translated that name in America.  The most common names, based upon the posts I read, are Yetta, Etta, Jennie and Henrietta. 
*There is a Yetta Meltzer, born in the US in 1903/died 1987 who is not the person I am searching--different family.*
I am not aware that her mother or two brothers emigrated to America.  
I do know the burial locations of the other Halpern/Hartenstein family members in the Horodenker, Progressive Horodenker and Zion's Bruder Bund landsmanshaftn in various Brooklyn and Queens burial cemeteries.
The most promising approach, I think, would be to:
1. search through all the appropriate marriage records (most likely focused on New York), 
2. search the Social Security claims index in the hope of finding the parent's names,
3. search naturalization files; unless she got married right away, she would have needed to go through the naturalization process (assuming she lived long enough).
Am I missing another strategy?  She is proving to be hard to find after her arrival.
Rod MacNeil
Philadelphia, PA USA

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