I have a few more verses to the Plymouth version which I think add to the coherence of the story

After verse 4:

Oh Willy, Oh Willy, oh pardon my life
And I will never covet to be your sweet wife
I will travel the country to set you quite free
Oh pardon, oh pardon my baby and me.

No pardon I'll give thee, no time for to stand,
And with that he took a sharp knife in his hand
And he stabbed her, and he stabbed her, 'til the red blood it did flow
And down in that grave, her fair body he did throw.

And he's buried her so deeply,and he's buried her so sound
Not thinking that this murder would ever be found
And he's gone on board his ship to sail the world around
Before that the murder should ever be found.

(The above are all from Jackie Oates' version, I think, but I found two others which explain how the Captain knew about the murder)

Our ship had a Captain, a man of courage bold
And late, late last night he went into the hold
Where a beautiful maiden to him did appear
And she carried in her arms an infant so dear.

And the dress that she wore was covered all in blood
So he quickly stepped up to her to help if he could
What man has done this deed? he quickly did say
But then in an instant she vanished away.