Coming in late, but just adding my agreement to a lot of what has been said above. I have done only a little recording, but in a couple of the songs I have done, I was doing them late and night (and don't usually trust folks to sing the harmonies correctly), so I overdubbed and sang a trio with me, myself, and I. I had the same thing happen that you are describing, and I couldn't do a whole lot to get rid of the effect until I re-recorded the same harmony, but singing differently. It ended up sounding bad because the harmony was, as has been described above, a "happy" one and when I sang it dark it sounded worse. So all that to say, if your singer doesn't want someone else singing her harmonies (and I do understand that feeling) and she is set on the harmonization, she will probably have to fix the problem on her end for the best result.
Of course, I could be all wrong........I am still fairly new to the technical side of recording.....
Of course, I could be all wrong........I am still fairly new to the technical side of recording.....