This song appears to blend information from a couple of Arctic voyages. The Eliza Swan, Rattler, and Resolution were indeed lost in the 1830 season, but earlier print sources for the song focus on the losses of the 1819 season.
A. L. Lloyd's full liner note on Thar She Blows! tells one tale:
Sad events lie behind this most spirited of whaling songs. By the 1820s the relativity milder northern waters were fished clean, and whalemen were having to search in more distant corners of the Arctic, notably round the mighty and bitter Melville Bay in Northwest Greenland. In 1830, a fleet of fifty British whaleships reached the grounds in early June, a month before they expected. But the same winds that had helped them also crowded the Bay with ice floes and locked most of the fleet in, including the Diamond, the Resolution, the Rattler (not Battler) of Leigh (not Montrose), and the Eliza Swan. Twenty fine ships were crushed to splinters and many bold whalermen froze or drowned. The Eliza Swan was among those that got free and brought the sad news home. Our song must have been made only a season or two before that tragedy for the Diamond's maiden voyage was only in 1825. One wonders if the man who made the song was up in Melville Bay, the year of the disaster, and whether he was lost with his ship.
In this version, the Eliza Swan was not lost. Shepheard, Spies, and Watson did separate research for a 2005 album:
The Diamond was built in Québec in 1801 and brought into the Aberdeen fleet in 1812. The Aberdeen Journal of 18 March 1812 reports: “The fine new Ship Diamond, Gibbon [that is, with Captain Gibbon in command] sailed on Thursday last, for the Davis’ Straits Whale Fishery.” When she arrived back in August she had a catch of eleven fish. The ship went on a yearly voyage until 1819 when she was caught in the early autumn ice and lost while staying too late in the season. Fortunately the crew were all saved.
The earliest print sources for the tune seem to follow the second set of ships, not Lloyd's. The mudcat historians have threads here: When was the Bonny ship the diamond lost) and Bonny Ship the Diamond. Maybe there were just two ships with the name The Diamond. Though Wikipedia (among other websites) can be used to track many wrecks, not all ships lost in the 1830 Davis Strait storms are chronicled. According to one mudcatter's research,
1830 was the worst year in the Greenland Fishery. There were 91 British ships in the Davis Straits that year and 19 of them were lost, most of the others were damaged, and 21 returned without catching a whale. Details are in Basil Lubbock's book 'The Arctic Whalers', which, although it gives much detail about the whole of the fleet, fails to mention a whaler called Diamond, (Eliza Swan, Rattler and Resolution are mentioned).
The Grieg-Duncan version of the tune (~1905) mentions Aberdeen, The Diamond, the Harcles, and the Jean. Ord's Ballad (1930) mentions the Hercules (i.e. the Harcles), the Jane (i.e. probably the Jean), the Bon-Accord. It seems very likely that Lloyd's version (1937) is conflating two whaling seasons (1819 and 1830). It's easy to imagine that the song was known and added to around the time the Resolution and Rattler were lost, and hence Floyd's version may still have been sung by authentic fishermen.