Helen, I took from the reference to being 'smart' said by the old lady to be the same as calling one 'smart arsed' which is a bit stronger in today's language.
I understand the dry humour you mentioned but it doesn't tie in with the assumption that 'spruce' could mean a 'ruse' or 'trick' in the sense of the song.
Personally as I said I have never, ever heard the word being used other that being smartly dressed or the name of a tree.
There is a derogatory comment made about inhabitants of a certain town here who only wear a suit when they go to court and you could construe that as being deceitful, to fool the judge into thinking they are of 'good character' so in this case you could say being 'spruce' was being deceitful. A bit of a long, long shot, however, to tie up this explanation with the song.