My first thought upon reading about your dilemma was “I’d check the Bremerhaven & Cuxhaven church records for a surname that would sound similar to Piers/Pierce. It is my understanding the local LDS (Mormon) Family History Center’s (FHC) have German church records on microfilm. They also have copies of almost all microfilms held by German archives. Although I am not Mormon, when I have gone to the local FHC, the staff there was welcoming and helpful in my research efforts. In my experience in researching my own German lines, I found German church records to be a substantial source of information.
Some of the German surnames I was thinking might have sounded like Pierce when pronounced with a German accent to an immigration employee are:
Peters, Riese, and Reiss.
When I did a general soundex surname search for Piers in Germany at
http://www.familysearch.org, the spellings of Pierce, Piers, Persch, Perz all came up in the search as families in Germany.
I wish you every success in your research.
VC Piers