I managed to contact someone from the branch of my family tree that Granny came from who had traced out our connection to the German Cottas.  From this I learned the exact nature of my relationship to Johann Friedrich Cotta, who was the leading publisher of the German Enlightenment, as well as a personal friend of Goethe, Schiller, and other prominent literary lights of his era.
 
I also learned that the name Cotta still carried some cachet among contemporary Germans—not quite as much as names like Rockefeller or du Pont do for Americans, but still significant—and that his publishing company was still in business.  Intrigued, I checked it out online, and found that (a) its current name was Klett-Cotta, and (b) the material in its current catalog was…uh…somewhat different from the enduring literary masterpieces my ancestor had published.  Prominently featured on its website was a German-to-Elvish dictionary, apparently inspired by a desire to cash in on the recent popularity of the Lord of the Rings series.

I e-mailed the modern company, asking if there was anywhere I could find out more about the history of the larger Cotta family, and received a prompt and courteous response referring me to two individuals bearing the Cotta surname.
 
As it turned out, these two names had apparently been selected at random out of some sort of e-mail address equivalent of the Stuttgart phone book.  One was a woman who did scientific publishing of some kind, and had long wondered if she had any connection to the famous Cottas.  Another was a somewhat over-elegant older gentleman who was certain of his ancestry—and for reasons I can’t begin to fathom, began attempting to woo his female relative (much to her annoyance).
 
At this point, I couldn’t help but recall the saying that you might be a redneck if you go to a family reunion to meet girls.  But on the plus side, the lecherous old Cotta’s antics dispelled any worries I might have had about not being as sophisticated as my old-world counterparts.