Good questions all!

Most versions seem to have the woman asking to be thrown overboard - it's one of the odd things about this song. Hence my gut feeling that the song was originally about somebody dying in childbirth (although that subject does seem rather strong meat for the broadside trade).

As for the 'Jonah' sub-plot, I'm not sure any of the versions of it work. Certainly women on board ship were seen as unlucky, but would a woman - even a woman in labour - be so very unlucky as to jinx the wind? Then again, while there's at least one song where an undiscovered murderer supernaturally brings a ship to a halt, would a thief be bad enough to do the trick - or Baring-Gould's "undutiful daughter"?

As for swimming, all that rolling and tumbling suggests a dead or dying body to me, rather than somebody swimming for home. But then there's "she'll never stop swimming till she comes to some harbour", which is another deeply weird line - they're at sea, for heaven's sake. It would only really make sense if the woman was bewitched herself - or, I suppose, if the sea rejected the undutiful daughter... (My favourite bit of the Baring-Gould version is when the sailor asks her, "O why do you swim?" Beats the alternative, would be my answer to that.)

When I sing it I always assume the poor woman's lost at sea and the sailor is planning on burying an empty coffin to remember her by - although that's also rather odd, now I spell it out. Either way, I can't bring myself to have him say he's going to bury her.