Of course, I cannot begin this analysis without stating whether I liked this song or not. So I won't.
Moving on, I feel that there are definitely three layers to this song (obviously), from the three different aspects, or points of view given by the three parts. Having also looked up exactly what Sycorax is (on Wikipedia), I discovered an interesting fact that postcolonialists view Sycorax, unseen mother of Prospero, to be the voice of women recovering from the effects of colonization. The Patagonians, next, are figment peoples famed to be very tall, living on some Island. Sycorax also lives on an island. Parallax is perhaps the most interesting aspect of that verse, and the song in general, because it speaks upon the different effects an object has once the perceiver is in motion, or, rather, it's all based upon the perspective of the observer.
So who's the observer?
But after all this back-story, we come to my aforementioned guess at three perspectives, rather than two from what we see. The first part of the song is told in the supposed third person. But, rather, when inspected closer, we see the use of the word "we", which places it first-person. The second and third parts are first-person as well, and so the perspectives are based upon the emotional or mental state of the observer. And the motion we see in the song, or tale, is based upon parallax, or the change in motion of the observer, the single observer we have.
In the first part, we have the Observer giving background information, sans human beings, but rather bones of "cormorants" or animals, boats, and plants/flowers in general, i.e., the setting. And it serves to set the mood, and of course the setting. The first part is removed from immediate action. The second part is direct action, live action, and the Observer incorporates the Landlord's daughter, in a very dark manner, sinisterly. But sinister only as far as telling a simple tale of innocent girl, bad thief/murderer. Not much emotional depth on the Observer's part.
The third section is where we see a darker, even more sinister and bleak aspect of the Observer, as we begin to see his (or her) mental state. It's almost the lament of an insane serial killer, with some deep emotional, repressed issues. Even after killing the landlord's daughter, the Observer wants to remain with the body to "dress" the eyelids with "dimes," etc.
But the second stanza of that section, "forget you once had sweethearts..." etc., almost reflects upon the Observer's past. Now on the island, forget all your memories, all the good aspects of your life, and die like I've died. (Physically or mentally/emotionally.)
The island to me represents something like hell. Not physical, but definite. An existence on some plane of this world or the next, a mythical place of Sycoraxes and Patagonians, but a dark, doomed place for the unlucky, brokenhearted, dying, dead, etc.