All those dampers are therefor is to cushion the shock load on the sprocket when the bike starts its power stroke. I cant see how that will cause instability. My 250sx has no stability issues on tar and it has no cushion, mind you it is a mx bike. But road racing 2T remove them to save weight and there is no stability issues there.
All those dampers do is provide a smoother ride on the tar.
When was the last time you replaced your steering stem bearings and wheel bearings?
I had a problem of major instability on my 250sx, but was caused buy wheel bearings and a friend's instability was caused by steering stem bearings.