Why would 'Martinmas' and 'Scots Lord' give anything an ancient setting?
Martinmas was being celebrated in England at least up to WWII.

>>>who's to say the Pepys song wasn't 'Scotch' but Scottish?<<<
To make this look more plausible you would need to demonstrate that 'Scottish' as opposed to 'Scotch' songs were being sung on the London stage in 1666. I haven't come across any, but that doesn't say there weren't any.