It's a long shot, but they've paid off before. Knowing the old German custom (designed only to confuse and befuddle descendants, you know) of using second or third names instead of the given name throughout life, Hinrich could have been the second or third name given to your Hinrich DAMMANN.
I have in Germany, a Johann Hinrich DAMMANN, b. 9 May 1842, son of Klaus AUGUSTIN (17 Apr 1819 - ?) and Catharina Margaretha DAMMANN (19 Dec 1820 - ?). Catherine Margaretha was a very distant cousin through my MEINKE line, and I don't know what happened to her or her son, but many of her cousins migrated to the U.S. Midwest the same time as your Hinrich.
If you want to follow up on this, they came from the Hanover and Hamburg areas. Let me know if you want more information on this line, and I'll send you what I know.