FocalFrenzy -- What camera/flash are you using? This is one of those shots and situations that would really benefit from an off-camera strobe. One concept in flash photography is how far "above" or "below" the ambient lighting you are. If you turn up a strobe far enough and set your camera to expose correctly for the strobe's light, you can easily overpower the ambient light to the point where it won't contribute significantly to the final picture. I don't know if you have access to that kind of setup, but IMO it's the best solution to this type of problem. I would have put the flash on the side where the fluorescent is coming from and turned it up enough to completely overpower any ambient light. A reflector (car sunshade works well) on her other side could serve for fill-light.
