Think about adding a hairl

Think about adding a hairlight – something like this: http://www.amazon.com/Photograph-Continuous-background-lighiting-ePhotoINC/dp/B003YH2GH6

Softboxes work well for this sort of thing – It may not get rid of the shadow but it will lighten it up. The problem is that a light strong enough to eliminate the shadow completely may add too much glare on the object itself.