I don't really know a lot about references in music either. I remember that when a piece refers to another piece, they tend to use the same key and/or the same chords, or sometimes the same instrument. I don't know whether they are in the same key, but if one is major and the other is minor, I'd say there probably isn't a link.
I'm also not sure why David Arnold and Michael Price would include such a link since there's no obvious connection in the plot. There's a shooting bride, yes, but Amelia's motive is completely different from Mary's and the story is quite different too.
I did notice another link though: 'Do not forget me' and 'Did you miss me?'