I've just noticed appendix G of Lubbock's book - a comprehensive list of Peterhead whalers from 1788 to the 1870s. No Diamond! No Captain Thompson! (Captain A. Thom is the nearest). So my thought is that the Diamond is fictitious, although I would be pleased to hear of some real evidence. Album liner notes are often written authoritively, but they don't always show eveidence of good scholarship.
Many of these songs were written ashore by (basically) songwriters, than were written on board ship by whalermen.
The Balaena was a real ship, right enough, hunting for whales (mostly unsuccessfully), seals and walrus out of Dundee in the 1890s.