Great that you've traced Dunderbeck back to 1876! I've traced two copies of the 1876 book: Library of Congress (Washington DC) and Brown University Library, Harrison Collection (Providence, Rhode Island). Can someone near one of those give us the complete 1876 text? Anyone with access to the Research Libraries Database may be able to locate other copies. The details of the book are:

"Our Own Boys" Songster (25 cent song book no. 15)
New York: Robert M. De Witt 1876
192 pp., 17 cm

In 1976, a friend's father sang the version he learned in working-class Boston ca. 1935. My friend wrote it down and I printed about 15 copies (hand-set letterpress at the Pierson College Press, Yale University). Quite close to the 1894 version. Once I see the 1876 version, I will pass on any information that seems useful. I traced it back only to 1927 when I tried in the 1970s.

The name Donderbeck (modern Dutch Donderbek) is a Dutch joke, roughly translating as "Thunder Maw", suggesting he belches loudly. Speck can be Dutch (now spek) or German. Sauerkraut is German, but was anglicized before 1876.