Thanks for all the responses, here and privately, to my question. With this help, this is now my reading of the inscription:
Our Beloved Father
Our Teacher Rav Ari Leib son of
Shalom HaCohen Shochet vBodeck (Slaughterer and Inspector)
Died 11 MarHeshvon 5683
May his soul be bound up in the bond of eternal life
I now have follow up questions about interpretation:
1) If Ari Leib's father is a kohein, wouldn't that make Ari Leib a kohein? If so, wouldn't that be included in Ari Leib's "title"? Or was it considered implied?
2) Does the designation shochet vbodeck refer to Shalom or Ari Leib? I assume it belongs to Shalom but I'm unclear about the syntax of the inscription. And I've been trying to understand what was indicated in 1914-16 New Haven city directories where Louis Koshkin has "Rev" appended to his name. His son Harry, who was a partner in a local delicatessen, lived with him. Perhaps he had hung up a shingle as a rabbi or perhaps he was working as a shochet and/or inspector? He and my great-great-grandmother Chila arrived in 1906 after their adult children. Chila passed away in 1916 and is buried in East Haven. He shows up in the 1920 US Census living in the Bronx with my great-grandparents, retired. Louis passed away in 1922 and is buried next to Chila in East Haven.