Jonathan,
If spoof/burlesque/parody seem too strong, how about simple 'borrowing'. There was a heck of a lot of 'borrowing' went on in this period, particularly cross-Atlantic. Artists like Cowell and the minstrels were flitting back and forth. A lot of Harry Clifton's songs were stolen by Tony Pastor and set down as his own on the sheet music with no reference to Clifton (See Levy copies). Even up to WWII traditional tunes were being appropriated and claimed by pop song writers.

Steve