I have access to newspaper databases back to the 18th century comprising millions of pages of print. Also extensive book databases.

A search finds not one example of barges or other vessels called "hogeyes" in San Francisco or anywhere else. And as I wrote upthread in 2020, there are no "hogeye" barges in the Century Dictionary or the Oxford English dictionary either.

Thus the chances that the chantey (or the well-known American fiddle tune, the "Hogeye Man") have anything to do with barges are essentially zero.

A "hog-eyed man" was a man with squinted or small eyes. The evident existence of a slang sense of "hog-eye" was, in terms of the song and the tune, fortuitous.