I find it very hard to credit the assertion that Hugh Roberton “chose the romantic name Mingulay”. There are references in 19th century records, albeit slightly different spelling (no u):
Mingala in Francis Broome’s Ordnance Gazetteer of Scotland in 1882-84, and
Mingalay Island in John Bartholomew’s Gazetteer of the British Isles 1887.
The rest is correct re the Gaelic and Norse origins and the lyrics of the song.