If she was moving around, the phase effect will be changing, as you observed. This will be difficult to correct, but it's probably possible if you spend enough time on it. It will be tough to do this, because you'll have to time-stretch the tracks at the points where the change happens. And if she moved around enough, there could be dozens of these points. Eventually it may become a losing battle. (This is as difficult as fixing a drum track where the drummer drifts in and out of time!)
The obvious suggestion is to just record more takes, with greater care toward engineering. If you were charging for your time, she'd go broke. Call this what it originally was: a simple documentation take. The fact that it was a great vocal was an accident; accept it and continue performing. Next time, plan from the start to make it a keeper.
If she's a good vocalist, she'll get another great take. It may not happen for a while (or for several sessions), but it'll happen again.
Consider this: if she has poor mike technique, you'll never be able to make decent progress on a "keeper" recording: she'll move around and you'll hear it in the track. Have her use this as a lesson in the importance of careful mike technique. This skill is almost as important as her ability to sing and play. With this philosophy, you've both learned quite a bit from the recording.