Harry Lauder sang 'Scotch' but did not sing 'Mackie'. I would suggest this was an English attempt at spelling MacKay. I can guarantee nobody in Scotland would write 'Mackie' and pronouce it as Harry Lauder did, i.e. 'Mac eye'.
I think you've done a wonderful job in transcribing Luader's works, I am merely pointing out a few relevant facts (in my opinion).