You have found the secret: most balancing efforts are trying to correct alignment issues. If the center of gravity for each piece and element were on the central axis from the engine to the rear, there would be no need for balancing. Typically the pieces (some part, a shaft, etc.) is off the central axis. So people put on balancing weights to "realign" that C of G onto the axis. Its much easier to put the whole assembly back into alignment.
On the Aurelia - the little splines on the end of the shafts (early type) are getting a bit off and thus throw things out of alignment. One shaft got back to .006" overall, and the vibrations went away.
Some background noise is a different matter, and more related to resonances from all the sheet metal. Dampening with mats, rubber, etc. can help that - or let it be.
In one B50 (very original), setup by a man who really knew what he was doing, you couldn't tell there was a driveshaft at all in the car. If you are interested, some of this is written up at: <http://web.me.com/geoffreyg/Aurelia_Tips_/driveshafts.html>