First, the answer to the question:
To get rid of shadows in cycles, you can disable Shadow in the Ray Visibility of the object (not the emitter).
Those are not shadows you are looking at, they are reflections of the object itself.
You've created a very reflective, almost mirror like material.
Without changing the lights, here's a render using a diffuse shader on the object, the alleged shadows are gone....
Here's the same scene with a glossy only material, showing the reflections on the glossy sirfaces...