Well, there's "pastiche" for a song (or other work) "in the style of" but not sending-up (not the same as "fake!"), or "homage", a pastiche where imitaition is the sincerest form of flattery. Neither of these apply to Mark's case, but they may come in handy elsewhere. "Lampoon", "pasquinade", "spoof" all mean much the same as "parody"; "travesty" is a bit strong, unless you're being nasty.

Any other word-nerds out there?

Steve