I was interested to see what conversion look you were describing here, so I tried converting this photo using a variety of color filters using the hue/saturation adjustment layer method of black and white conversion described on this site.
Since her face is primarily a warm reddish-yellow tone, she will appear brightest against this background and have the least facial contrast if we use a reddish-yellow color filter. The worst, of course, would be to use a hue which is opposite on the color wheel: cyan-blue. Both are shown below:
left: cyan-blue color filter (darker face, higher facial contrast)
right: reddish-yellow color filter (brighter face, lower facial contrast)
Unfortunately, the top right is pretty much a best case scenario using standard black and white conversion. I agree that DanielJ's custom gradient/painting method is necessary here if you wish to be more aggressive about removing the shadow cast below the eye (since this shadow is pretty much color-independent). However, in my mind the above b/w image on the right still has somewhat less pronounced shadows on the face than in the color original...