Specifics, as always, are welcome. Thanks, guys.

It is not so much that these chanteys (not just the few I've listed so far, but the larger category) have "never" been performed, but rather that they have been performed so infrequently (or within such a limited area, as Ross suggested) that they are very poorly known to the chantey audience at large. The second part to this is, again, the issues of how the performances were created, i.e. whether they are imagined, as best as possible, from written text. I would guess that most of these recordings that one finds are recreations of the text.

The Bahamian recordings by Lomax present us with a slightly reverse scenario. We have these "authentic" versions, recorded for posterity and there is not so much of an issue of knowing what they are like (although more than one version is always helpful). Moreover, in several cases these recordings have been seized upon by revival singers and have since become both fairly well known and based on an aural source.

Abrahams' book is obviously the best source so far if we are just looking for Caribbean shanties, in conjunction with the more recent performances by the Barrouallie Whalers. But there are plenty of other chanteys that seem to have been popular back in the day, collected by Hugill, Bullen, Terry, Sharp, & Harlow that don't appear in these.

Out of the few listed so far, "Round the Corner, Sally" is definitely the most common, but I'm not sure if Hugill's significantly unique West Indian version is a part of that knowledge.

As a related note, one book that I don't seem to ever see mentioned, but which should accompany Abrahams', is Horace Beck's FOLKLORE AND THE SEA. He prints the following chanteys, having covered (in an albeit much more sketchy way) a similar ground as Abrahams:

Yado
Sam Gone Away
Ring Down Below
Ding Well
Mountains so High (related to Poor Lucy Anna / Louisiana)
Drive Her Captain Drive Her
Stormalong ("Yankee John" version)
Long Time Ago
Blow Boys Blow
Bulldog
Man o' War Sailor
Hilo
Rosabella
Old Moses
Pappy You Done Dead

Those being noted, the focus (for me) is not on "Caribbean" chanteys per se, it just happens that many of these chanteys in this category have been sourced from West Indian singers.