My 1763 edition of TTM has the same version as in my reprint of SMM with just a few minor alterations to spelling, e.g. Graham/Graeme. It's at Vol 1 p230 but I can't see a parody. I don't think it's in my edition. If it's only 4 stanzas could you post it for us please?

Regarding the line
It fell about the Martinmas tide, Scott made good use of it in his 'Jamie Telfer'.

Of course 'Lammas' soon translates into 'Martinmas' as the doughty Douglas would know.