In "Chiefly About War Matters" published in the Atlantic Monthly, Hawthorne posits:
There is an historical circumstance, known to few, that connects the children of the Puritans with these Africans of Virginia in a very singular manner.
They are our brethren, as being lineal descendants from the Mayflower, the fated womb of which, in her first voyage, sent forth a brood of Pilgrims on Plymouth Rock, and, in a subsequent one, spawned slaves upon the Southern soil...
The Slave Voyages database shows no record of such a voyage, and histories of the Mayflower are vague of its service between its time on Cape Cod and its eventual appraisal and breaking on the Thames a few years later.
Where did this idea originate?
Wendy Warren references this at the end of New England Bound, literally as her closing paragraph. She quotes Hawthorne and then:
Several ships named Mayflower set sail from England's ports in the seventeenth century, and one of them took slaves to the Caribbean. It was not that of the famed Pilgrims, which was already on its last legs when it arrived at Plymouth. Hawthorne was mistaken in thinking they were actually the same ship. But in metaphorical terms, of course, he was absolutely right.
She sources the quote, but doesn't have a citation for the facts. Damn it. I've seen confusion like that in nineteenth century sources, and fallen victim to it once or twice, so I believe her. But it's but still a dead end. Sorry.