We share the same ancestry you outlined below. Beyond the lineage you shared from William and Hannah Smith Burleigh, were John, William, John, John, Louise (my Grandmother).
I found your post searching around for background on the Argentine/Uncle Oliver Cromwell connection. Found this:http://books.google.com/books?id=dphAAAAAYAAJ&printsec=f...
Further support for your search; but I've found little else besides conjecture. Please drop me a note if you have additional information or wish to share further information about the Burleigh line.
PS: I traveled to Scotland last Summer with my Son; visited Burleigh Castle... Google it ;-)