Got Schmeelk?

I am looking for some help in solving another family mystery involving my 3x great-grandmother.

Her name was Katherine Maria Schmeelk, though the spelling could be Katherine or Catherine and the note on the back of the photo says Marta instead of Maria. She was born around 1834 and died in 1901. Katherine married my 3x great-grandfather Adam Arth, an immigrant from Hesse-Darmstadt, Germany. Within his lifetime the name Arth became Art. 

In with the photo were two obituaries for Schmeelks that must be relatives of hers. One was from the N.Y. Times in 1935 for a Herman Marcus Schmeelk from Hanover, Germany, who had settled in Rockaway Beach, NY and was referred to as a "pioneer developer of oyster and clam beds." At the time of his death only two of his children survived, son Garrett and daughter Kathryn. 

Sounds like Kathryn is our person, right? But no. The second obituary was for Kathryn G. Schmeelk, daughter of Herman, who never married and never left Rockaway Beach, NY. As Katherine/Kathryn/Catherine was a VERY popular name for German women at the time, it is my best guess that Katherine and Kathryn were cousins. 

Except that Herman would have been born in 1850, about 15 years after my 3x great-grandma Katherine. So they could have been siblings? Cousins?

Ancestry has not been much help. They keep trying to push her father as either Blume or Seibel, both of whom did have daughters named Catherine of a similar age and both hailed from Germany, but none of the records for Katherine and Adam that we have line up with their families.

I am left with assuming that my Katherine is related to the Rockaway Beach Schmeelks, and according to Herman's obituary, his parents John and Catherine (Piper) Schmeelk brought him over as an infant from Hanover, Germany. I am starting a search both assuming and hoping this is the right family and maybe I can find her if I trace a lineage down from John.

It is always possible that Schmeelk was her married name before she wed Adam Arth, but there is no evidence to support that theory. And then it would be strange, for the time, for her to keep tabs of her former extended family. But I am keeping my options open.

I can't find any definitive records on her except for this notation on the back of her photo. But I'm trusting the family notes until I learn I can't and I'm writing this post in the hope that maybe someone else is looking for her family, too.

If anyone has any tips or knows of any specific German immigrant sources to search, I would appreciate any and all breadcrumbs.