I have used the periphery ring clamp on my VPI TNT-6 for over four years now. The ring clamp not only flattens any warp out of your LPs for better tracking of your cartridge, but it also is important to the overall voicing of the VPI turntables.
When I transitioned from the acrylic platter and Mk. V center clamp to the periphery ring clamp, I found the sound took on a more natural and fuller bodied sound with the ring clamp in place. By comparison, the turntable sounded somewhat analytical when using just the Mk. V center clamp with the acrylic platter. Since that time, I have upgraded my platter and bearing to the heavier "Super Platter." However, I have not done any fresh listening comparisons with and without the ring clamp with the new platter.
As for the role of the belts, around the perimeter of the ring clamp, I believe their purpose is to dampen any ringing of the metal clamp.
Why don't you do some listening with your new clamp in place and tell us what you are hearing with and without the clamp?