It seems I got two songs confused.
The actual song that I was thinking of in my last post was the theme from Love Story (many thanks to those who helped me figure that out with a crudely made midi I plunked out at midnight after being woken by the nagging realization I'd gotten two songs confused).
See, it's not that the songs themselves are similar, but that they evoke a similar emotional response. And while one grandmother had Swan Lake on a music box, the one with the roses played the theme from Love Story.
While I love both, the particular arrangement of the song on that cheesy fiber-optic music box was by far the more beautiful. Problem being, it wasn't quite fully accurate to the song, so I'm not sure if all music boxes will play it that way should I order one, or if I am going to have to become a finicky pest and go on a hunt for the right version.
The song, for those unfamiliar: