My best guess and that is only what it is that the family remained on board and continued to New Orleans.
How do the dates jive?
Where did you find the information?
Have you looked at the Hamburg emigation list? I know that you can search the LDS film at the county library in St. Louis. It is on permanent file there.
My great grandfather departed Hamburg 1859 and went to New Orleans. The book Germans to America says he went to New York arriving on 6 Jan 1860. An index card from the New Orleans Custom House says he arrived New Orleans, La on 6 Jan 1860. At the moment I can't put my hands on it but I also have a copy of the passenger manifest that said he went to New Orleans.
Do you live near an LDS library? Near St. Louis?
Max
Taking a ship from New York to New Orleans to go to St. Louis WOULD make sense. Or to Perry County.