Would the construction of the double cardan joint itself have any impact on vibrations?
Considering that we know that a single u-joint at an angle does not result in a 1:1 ratio, but two u-joints cancel each other out over the span of the joints, that would mean that the double cardan intermediate carrier must accelerate and decelerate twice with every rotation of the driveshaft.
View attachment 165109
A larger intermediate carrier, such as a 1350 carrier, is going to have significantly more rotational inertia than a smaller carrier like a 1310. Not only does the 1350 have additional mass, it has a larger overall diameter, both of which increase its rotational inertia. But it must angularly accelerate and decelerate the same amount as the smaller carrier. So in theory, a 1350 DC shaft should have significantly more vibration than a 1310 DC.
This vibration would present itself as torsional vibrations, so balancing of the driveshaft would do nothing. A properly tuned torsional mass-damper could negate it, but I doubt the factory harmonic balancer is correctly weighted and damped to effectively do so. Since the rest of the shaft travels at a relatively constant speed, no mass can be added to the shaft to effectively counteract the vibration induced by the acceleration and deceleration of the DC joint.
There would only be a few ways to reduce or eliminate this effect.
The first, or most obvious, is to delete the driveshaft. This is not practical, so I will ignore it.
The second would be to use a double-double cardan driveshaft, or a driveshaft with DC joints at both ends. If the DC joints were installed 90 degrees from each other and run at the same angle, one intermediate carrier would be accelerating at the same time as the other one would be decelerating. With a sufficiently stiff center tube, these accelerations would cancel out, and few to no torsional vibrations would leave the shaft and enter the transfer case or differential.
The third option which I briefly suggested earlier would be to ditch the double cardan joint for a true CV joint like a Rzeppa joint.
View attachment 165108
Unlike a double cardan joint, a true CV joint like a Rzeppa has no parts that must angularly accelerate or decelerate. Thus, it will not create torsional vibrations like a double cardan joint will, especially at extreme angles.
This effect is actually called out in the Wikipedia page where I got the images from. Scroll down to the section on double cardan joints.
https://en.m.wikipedia.org/wiki/Constant-velocity_joint
"Double Cardan joints require a centering element that will maintain equal angles between the driven and driving shafts for true constant velocity rotation. This centering device requires additional torque to accelerate the internals of the joint and does generate some additional vibration at higher speeds."