Now that I have time to look into this further, and an enjoyable pursuit it is too. I have found a few things that may help marginally.

A Google search of "Galla Water" give many sites with various but very similar lyrics for this tune as well as several midi files, all of them are simple variations of the melody.    Since I can't read music well enough to tell you if any are different from the midi file in the site directed to I suggest you do the search as well.

The lyrics are almost universally atributed to Robert Burns and the melody used is titled "The Brave Lads of The Galla Water." This melody is clearly not related to Brian McNeills fine song. But it is the title and melody used by the Corries. As to other tunes attributed to this title I am unable to find them.

A further suggestion is to looki into Robert Burns for more definitive information as he appears to be the lyrical author atleast.
This is probably lucky for you because I can't think of a single person that is more annotated and footnoted than Mr. Burns. There is sure to be a truly scholarly effort put into his melodic choices and the previous histories of the melodies as well.

Good luck Lute

Don