You don't need a reflect node for this. The "Background" channel of the Reflect node is just what is used when the Reflect node cannot find something to hit.

To force the reflection of an image map in the material, just connect the Sphere_Map to the Reflection_Color. (Or any channel, really. The Reflection_Color is just added to the final render the same as Refraction_Color, Alternate_Specular, Alternate_Diffuse, and Ambient_Color) No ray-tracing or reflection is needed for this calculation.

You can use the same exact equirectangular images with my Environment Sphere or with the Sphere_Map node.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)