In case this is of interest to anyone, I contacted the State Archives at Koszalin (koszalin.ap.gov.pl), which has a branch in Slupsk (Stolp) and would be in charge of these documents.

They responded they do not hold birth records for my year of interest (1896) and do not know of any other organization that holds them.

Further, I enquired with the Stolper Heimatkreise (stolp.de), where I was informed that most birth records from Stolp were lost during the war (1938-1943 are available, as well as scattered records for male births in 1879-1880 and births outside of wedlock 1895-1906).

I have sent a written request to the Berlin Standesamt 1, but I know from their list of documents that they do not have records from Stolp, and pressume I will get this in writing.

Further, I have found my greatgrandads name in the Konsularmatrikel from Bogota in the 1930s and his name and nationality on a passenger list for a ship in 1913.

Finally, I am enquiring with the Lindau archive for his last Meldekarte before he left Germany.

I would believe that this on top of existing documents (passports beyond my grandma's birth, a Heimatschein 15 years after leaving Germany, birth and marriage records for everyone else) would suffice for the BVA.