How to create a backgound-independent transition?

[Contours]

I've been trying to create a fade-style edge transition that works regardless of the background the object is placed on. I've tried the blend tool and the shadow tool.

The blend tool gave a good result on a colored background, but it was terrible when the object is moved over anything lighter. The shadow tool was better at handling differences, but I can't find a way to make the shadow the proper color. I need the object's color to just edge-fade into whatever background it is on.

Any suggestions will be appreciated.