Don't remember but didn't Worf comment that Klingon Opera was awful? I'm all for adding killer KDF music though.
Maybe switch Fed music with something to make them feel all warm and fuzzy. Or as a Apr 1 joke give them the Jewish Mother voice who nags them about their shields being down or how they don't communicate with their mothers : )
I must admit I was pretty disappointed that the music didn't change at all when I made a Klingon - it really added to the sensation of 'you're rolling another character that is a bare facsimile of a Starfleet one'.