I'm hoping someone can offer insights that escape me. It seems that Ethiopia gained a lot of reference in the mid-19th C minstrel genre......"Ethiopian Glee Book", Ethiopian Serenaders, Ethiopian Delineators, Dumolton's Ethiopian Serenaders, New Orleans Ethiopian Serenaders, Buckley's Ethiopian Serenaders, and eight pages of "Howe's 1000 Jigs and Reels", containing 47 melodies under the heading of "Ethiopian Melodies". YET, being in eastern Africa, Ethiopia supplied very few of the number of enslaved people of southern U.S. that minstrel shows portrayed. So.......why "Ethiopian"?
Pure speculation, of course:
The human head is attracted to certain words because they're fun to say. We've also tended to use polysyballic verbiage as a source of class humor...educated vs not. I think the humor there is in the idea of such a florid name tied to slaves. We see similar humorous naming conventions in slavery as well: Pompey, Napoleon, etc.
Our (euro/white/whatever) idea of Africa in the 19th century was very limited. Few specific areas had recognizable names, mostly states on the Mediterranean. Most of it was a mystery, being explored...and exploited. Fabled lands and cities were the fodder of pulp fiction writers, so we get Kush, Timbuktu and Ethiopia (among others). Ethiopia was also known as a Christian empire, so it may have been more 'acceptable' to white ears because of that.
Thanks for your "speculation" which I think has some merit. I also asked a couple ethnomusicologists/archivists who are not on this list and one said, "It was probably meant as a euphemism for "African," not a literal word for the region. I suppose it came from Classical or Biblical sources.", which sounds similar to your speculation.
Ethnomusicologist, Paul Tyler, responded via email with, "Off the top of my head I would guess it due to European American's profound ignorance of Africa. Even though an estimated one million ante-bellum African-Americans had actually been born in Africa, the intellectual demands of maintaining the peculiar institution required such ignorance. On the other hand, Ethiopia was an African empire that Westerners could not ignore. It appears in the Christian bible and contributed much to the development of Western civilization. (So did Egypt, but most Westerners treated Egypt as Mediterranean and not African.) It wasn't until the Conference of Berlin in 1885 that cartographic boundaries were imposed upon the African continent, as the European powers divvied up Africa into colonial possessions."