I gave it a quick 5 minute run through with Ps. Getting rid of the black corner is just a matter of using the selection tool to select it and then fill it with white. Then I used a copy of the blue channel to make a mask of the ring; using a levels adjustment on it to get a solid black and white, then using a brush to fill in the highlights. Using this selection to make a mask on a curve layer I then boosted the mids till the background was white. After that I used the patch selection tool to get rid of the wax, replacing it with the bottom of the outer band and then using the free transform warp tool to align the shifted section of band. Some quick dodging on the bands and then a levels layer, another curve layer (set to luminance) and then an inverted surface blur layer and a double high pass to really bring out the detail. I didn't bother masking them or fine tuning their opacity because for this purpose it doesn't matter.
http://s103.photobucket.com/user/volvo-1/media/IMG_4162_zps9c5abbf8.jpg.html
As far as the image itself goes, I don't like that the back of the ring is soft. I would recommend using focus stacking, or getting a tilt shift lens, or adapting a large format camera. Any of those three options would allow you to get the entire top of the ring in focus for a shot like this. I also think this ring would look better against black acrylic, the silver/white gold would stand out much better that way. Another thing to keep in mind is that if you have reflections that you're having issues with, sometimes it's actually easier to relight the subject specifically to deal with the problem reflections and then merge the two exposures in post. Anyway, that's just my two cents.