The axle stand test has been done! Here is what we learned:
Putting the truck on axle stands and running it with the rear wheels off the ground makes no difference. The vibration and noise is still exactly the same. This eliminates the front suspension and tires as the problem. The engine has previously been eliminated as engine speed has no impact whatsoever on the noise or vibration.
Removing the rear tires/wheels makes no difference at all. This eliminates them.
Here is where it gets interesting! Our first step was to use a metal rod to feel for vibration. The rear axle and differential was very steady at every point we touched. The tailshaft housing of the transmission was not steady at all. Next we used that same rod and laid it against the spinning surfaces to see if they were spinning true.
When the rod was placed against the spinning companion flange on the differential (where the driveshaft attaches to the differential) the rod sat smoothly against the spinning flange, indicating that it was spinning true.
When the rod was placed against the spinning driveshaft however, it was a different story. The driveshaft was definitely not spinning true as the rod bounced and could not be held smooth. We tried this test at 3 points on the driveshaft, with the same results each time-the rod bounced like mad.
We also put the rod against the spinning slip yoke where the driveshaft enters the transmission tailshaft and it bounced there as well, although not as badly.
I had previously checked the fit of the slip yoke on the tailshaft and it appeared good. No wobble and it had to be lined up nice and straight in order to slide the slip yoke in, suggesting that the fit was correct. I did however note that if I grabbed the slip yoke, I could move the transmission output shaft up and down a bit. We did some measuring, and it appears that if I grab the slip yoke, I can move the output shaft up and down and the range of motion is about 0.052 inches.
Here is where I can use some advice. Is the 52 thousandths up & down play normal, or is this the source of my vibration and noise. Or is it simply a bad driveshaft. Any input here would be appreciated!