The General Jackson song is great because it shows "Fire Maringo!" was sued for both rowing and stowing, which means that it (or its "frame") was reasonably well known and not a one-off imprtovisation. Also, it eventually turned into "Santa Anna," a classic shanty. (With the evident substitution of "Monterrey" or "Floriday.") I believe Jackson's Tennessee militia was in West Florida in 1813 in the Red Stick War. Or so ISTR from Disney's Davy Crockett show.

So there's proof that the move from rowing and/or stowing to heaving happened at least once. Until Gibb's discovery, it was only a reasonable conjecture.