Fascinating...you have a rich storehouse of family history!
About Charles Scheffel, a witness to the 1865 marriage of Friedrich Gottschalk and Anna Leininger - he might be a brother-in-law to Friedrich Gottschalk (I haven't found proof of that) as he is married to an Anna Wilhelmine Gottschalk. If so, then tracking this couple back to Europe would provide another way to paddle across that ocean.
Anne Gottschalk married Charles Scheffel 27 July 1855 in New Orleans - and here are a bunch of additional possible siblings to Your Friedrich Gottschalk:http://nutrias.org/inv/jpmarrindex/bgoo_gow.htm
The "possible siblings" list is important as it may be the single best way to differentiate various people of the name Friedrich Gottschalk who were born ca 1840s in Prussia.
BIRTHS to Anna and Charles
1856 Pauline Johanne Henriette Scheffel
parents John Charles Scheffel and Anna Wilhelmine Gottschalck
1867 Emma Scheffel
parents J. Karll Scheffel and Anna Gosthaulk
1871 Mary Scheffel
parents Charles Scheffel and Anna Gottschalk
1869 Carl Scheffel jr.
parents Carl Scheffel and Anna Godtschalk
Charles can often be a variant of Carl, so it could be the same couple in all the births (Alphabetical Birth Indexes for Orleans Parish 1796 - 1900). LINK: http://files.usgwarchives.net/la/orleans/vitals/births/index...
Children Emma, Charles, and Marria in this 1880 census record, below, match the births above. From Ancestry.com.
New Orleans, Orleans, Louisiana
Annie Scheffel 48 born about 1832 in Prussia
Bertha Scheffel 21 b about 1859
Annie Scheffel 18 b abt 1862
Mathilda Scheffel 15 born about 1865
Emma Scheffel 13 born about 1867
Charles Scheffel 10 born Louisiana, parents both b Prussia
Marria Scheffel 8
Emma Ewalds 13
John Charles Scheffel born Prussia
25 Jun 1867
The name "Annie Scheffel, Widow Charles" appears in New Orleans city directories.
A Jno Charles Scheffel appears on Passenger and Immigrant Ships List index that won't open for me...
A Charles Scheffel died in New Orleans in 1877.