Your NOS u/joints, if dry stored in the original packaging, are likely fine to use.Would like to know more about the process since I need to do the exact same thing...was it hard to get the middle carrier pillow bearing off? Did you get a kit with the u joints, pillow center bearing, and the rubber one behind the Trans?, I already have new u joints and the rubber one behind the Trans but they are old NOS parts so I wouldn't rule out just getting a new kit...your making great progress on your spider!
The rubber coupling behind the transmission is probably fine to use also providing there are no signs of cracking or separation between the metal bolt tubes and their surrounding rubber - be aware that modern replacement parts may not be as good or last as long as original NOS parts.
Don't worry about failure of this rubber coupling, the front sliding section of the driveshaft has an extension piece that passes through the rubber coupling and locates positively on a small bearing ring on the end of the transmission output shaft, (at least it does on manual transmission cars, (idk about automatics, as I believe your car is?), so it can't drop down and hit the road, as I explained in an earlier post.
But do check out and replace if necessary, the d/shaft centre bearing and it's rubber mounting and also the transmission rear rubber mounting/support.
It might be no harm to consider also replacing the engine rubber mountings also if the car has been sitting for a long time (I think you said 12 years).