Burlesque essentially is satirising the original song or genre. I need to look at these examples more closely. I've not seen Scott's 'Twa Corbies' described as burlesque before. Scott was far too serious for burlesque anyway. Scottifying English songs and ballads seems to have been a hobby north of the border from about 1750 to about 1830. Some of Motherwell's contributors were certainly accused of this. McQueen? I think 'Douglas Tragedy' is a perfect example but that's just a hunch. Not a lot of proof around for such matters any more. 'The Corbie and the Crow' certainly looks worth following up.

Not sure if Henry and Sid were satirising the originals. More like parodying I'd say, but I'll give it further thought.