One of the reasons you weren't happy with using a color fill approach is that the problem in those areas is not so much color as it is tone (ie, brightness). When the brightness of an area is that low, odd things happen to the color.
Other than reshooting the image with better lighting and a better lens (...which I highly recommend...), probably the easiest way to get closer to what you want using only post processing is to bring the image into ACR (or LR), go to the adjustment brush, put a "pin" in one of the darkest areas (as shown), and use the settings as shown to paint the remainder of the dark areas.
It's natural that even after lightening the dark areas, their saturation (ie, strength of color) will be more than other parts of the gem. That can also be adjusted, but I wouldn't go too far with that, otherwise it won't look natural.
HTH,
Tom M
PS - I took the liberty of spotting some of the imperfections in your image. I couldn't tell if they were dirt on the surface (which is OK to remove in post processing), or inclusions (which probably shouldn't be removed so as not to mislead the buyer), but I removed them anyway.
