To clean up shadows from a white background, I use the Burn tool, set the drop down to highlights, and depending on the strength of the shadows I will go from a really bad background (gray) at 50%, to light shadows around 6 to 8%, when you get near your subject, drop it to 2% and you can overlap midtones, without damaging the edges.
I alter the size of the brush, starting with big areas at 340 pixels, reducing as the area gets cleaned up down to 5 to 10 pixels.
Best of luck, have you tried an exposure compensation, similar to compensating for snow or sand, that might help to slightly overexpose.
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