As I recall Yamaha had a kit to mount the fairing to the frame. My 4bb has a frame mounted fairing. I had it up to about 120mph and it's not unstable at that speed. That's including the leaking fork seal (and probably by now empty left fork leg :) )
But it's an old design, it will never be nowhere as stable as newer bikes. Crosswinds have a disturbing influence on these, and at least my, bike.