"... and who says 'zince'

People in Zummerset, where the Zider apples grow.

My impression is that when speaking Scots pronounce "syne" to rhyme with "tin" rather than with "fine".   Clearly, it's got to be the latter in Burns's song, to sort of rhyme with "mind", but does this indicate that there's been a shift in pronunciation, or was he cheating? (Or is it just that the Scots I know have lived in England too long - or too lang.)