JffB, hi, my research was about orality versus literacy and the transmission, however corrupt, of Tannahill's chosen tune in 1807 when he wrote the song, against the printed version supplied by Smith in 1821. The printed version came out on top as it was published by all the big houses throughout the 19/20 century with piano accompaniment and so it is sung today.
I showed that the Tree Carls tune existed through oral transmission and was used for the Bonaparte song (Watt says so) and as it was untitled (oral transmission) it became known as (Isle of) St Helena.
I didn't look into the lyrics or history of the Bonparte song so can't help you there.
Mary Black sings, I would say, a 'corrupted' version of The Three Carles as the second part shows its origin compared the standard tune of the Braes published by Smith in 1821.
The tune, Braes of Balquhither is very old and was first vocalised by Burns "I'll Kiss Ye, Yet" but Smith put it into the form we know today.