While not in answer to your query, one fact drew my attention concerning your g-g-grandmother Rochel FRUMKIN.
I am researching the BRAUDE family from Kelme, Kovno, Lithuania, including the rabbinic BRAUDE dynasty.
You wrote: "The attached documents indicate Henry was born in December 1882, but it's possible he could have been born a few years earlier or later. His father's name was Zvulun Lieberman (note that his death record lists his father as Julius) and his mother's name was listed as Rochel/Rachel (maiden name listed as Frumkin)."
On my tree is a Rabbi Shmuel KELMER (1798-1867) one of whose wives was Frume BRAUDE (1815-?). The children of this marriage took the surname FRUMKIN, presumably in honor of their mother Fruma. I do not know how widespread is the surname FRUMKIN, but there may be a connection between your g-g-grandmother and the FRUMKIN family from Kelme.
For others reading this message who may be knowledgable of the FRUMKIN family from Kelme, I would welcome corrections. The dates associated with my FRUMKIN tree members are somewhat inconsistent and contradictory.
Porter Ranch, CA