Personally I think those reflections are just too distracting. I'd go for a much less reflective background and draw the eye using shadows instead. Of course the rings should be well lit to create a shine, but the reflections just distract me from the real object.
You should gel your background to make it more appealing, and put more light on the walls around your subject so your strobes cover more area around the room.
When photographing a subject and a reflection, focus on the subject, then the reflection. Then work out the distance between the two points using the lens distance scale. Then check the hyperfocal point, close the aperture accordingly and shoot. Better lighting though would be a good idea.