Well in hindsight I can tell you that its not good that you bought the bike with this problem as a preexisting condition, which make it suspect that the previous owner knew something that you did not. When you say that the crank and carbs have already been balanced, I hope that information was not also passed on by the previous owner, if so that is also not a good sign. A 2004 B12 should not have this problem this early, the only thing I would try for starters, if you haven’t is to synchronize the carburetors again and while at it check for vacuum leaks around the carburetor clamps.
PS- I hope your not talking about a minor vibration in the fairing vibrating against the frame because that is a common occurrence. So I am assuming your talking real shake type vibration that is physical and obnoxious and not buzzing.