Coming back to the balancing issue, I am in doubt that the drive shaft would be out of balance. We can assume that, when the car left the factory, the drive train was balanced and without vibration. Later, the drive shaft does its work for decades and is only touched when a removal of gear box or rear axle is due, or a change of the flexible couplings is in need. Although the part is subjected to great torsional loads at high rotation speed, there is no wear at all, provided all the bolts are kept tight. Therefore, I cannot imagine how the drive shaft can become unbalanced, except maybe when damaged in a ground strike or similar when it gets bent or distorted.
On the other hand, the flex couplings are subject to wear and are replaced now and then. There are a few organisations and persons making aftermarket flex couplings in small numbers. We don't know if there are original specifications as to the material used, are avaliable. Sometime couplings are made using an old part as a template. It might be worthwhile to have a close look at the couplings. With some effort an adapter could be made to check balance on two parallel knide edges. After all, the flex couplings are spinning at the same speed as the drive shaft, but with a much larger diameter. Also, all the bolts and nuts attaching the coupling should have the same mass.
Back in 2013, Morris Parry has published a detailed instruction for making flex couplings for those who want to try. He does state the material as "Rubber disc". (The Lancia Augusta newsletter, Issue 9, March 2013)
Next week, I will put my car on jacks and will remove drive shaft and couplings. I will let you know my findings.
Just MHO Karl