I did a few driveshaft rebuilds years ago and one recently as an emergency repair for a friend. These were light to medium truck dirveshafts, so no idea as to how fast they ran. What I did was to salvage the yokes by cutting thru the weld that held them to the driveshaft tubes. I cut the tubing off fairly close to the yoke and chucked it in the lathe. I indicated it as best i could, and supported the yoke on a tailstock center. Using a sharp toolbit, I was able to turn thru the weld and re-establish a square shoulder on the yoke.
The tubes had been pretty well "wound up" or bowed. Having the yokes cleaned up, I then fitted theminto new mechanical steel tubing. The yokes had a good boss or pilot to drive into the tubing, and had a square shoulder. I cut the tubing on a band cutoff saw and then cleaned it up with a facing cut using a steady rest.
I was lucky in that the yokes had centers in them. With the driveshaft supported on centers, I then put my ground right up close to where I was going to weld. I "quartered" the shaft and put on four tack welds, going 12:00, then rolling the shaft to 6:00, then rolling to 3:00 and then to 9;00. I was using 3/32" diameter E 7018 electrode and ran just the smallest tacks. I checked the shaft for true and things were probably within about 0.010-0.015" TIR. How much of this was due to bow in the tubing and how much was due to things cocking was something I didn't bother to find out. I had some cold drawn mechanical steel tubing (I believe it was "DOM" or drawn over mandrel) for making the new driveshafts. How straight it was as-received is also something I never checked.
After I had both yokes tacked on, I then welded my root pass. I did this also by breaking the root pass into segments and doing it in a sequence wiht a "backstep". I ran a cover pass in the same sort of sequence. This didn't take things any more out of true.
Not knowing what else to do and having no means to do a dynamic balance, I did a static balance with the shaft supported on the lathe centers. I spun the shaft by hand and marked where the heavy side was. I did a few such spins and got a consistent heavy side. I took some nuts and duct taped them to the light side as trial weights. When I got things to balance out to where the shaft would not stop in the same place twice, I called it balanced. I then weighed the nuts and cut some steel flatbar of a little more weight than the nuts. With some grinding, I had the flat bar weighing what the nuts had weighed. I tack-welded the flatbar to the driveshaft tube and verified the thing was still in static balance.
I have done this on a few shafts. I wonder about blancing out of plane, since the shaft will run at an angle and I was balancing with the shaft laying horizontal.
As I noted, these were fairly short shafts for light trucks. That was almost 30 years ago. One truck was an F-250 and the other was an old Cornbinder Scout.
The last driveshaft I repaired was for a 1946 Dodge dump truck. That was about two years ago. Nothing turning very fast. The old Dodge gets around at about 45 mph when my buddy runs it to haul firewood locally. I guess the shafts ran OK, as I never heard any complaints of vibration from the people who drove those trucks.
I also modifed a couple of AG PTO shafts. These had to be shortened. These used a square telescoping section rather than a spline. The fit of the square telescoping section was none too good. I shortened things up and rewelded. These shafts never looked to be blanaced, and I saw no real way to do a static balance. Running a 6 foot snow blower or a bush hog at speed on a tractor PTO with a pretty good angle on them, these shafts run with surprisingly little vibration.