[Tom Goldman]

Looking at the second video ,it appears that there is very little pinion angle.
It may be decieving due to the camera angle, but it looks fairly shallow.
Considering it looks like a 3" mild steel shaft ,harmonics are a possibility.
I would at least try increasing the angle by 1-11/2 degrees to see if it has any effect.
I used to deal with this type of transient vibration on Jeeps and usually small amounts of angle change corrected the problem.
I also noticed what appeared to be a small ammount of play in the u joint at about 27 seconds, but that might just be the camera angle.
One other thought, if the trans yoke is one of the Spicer forged pieces , I'd check to see if the splines are twisted.... I've had at least three of them on cars with enough twist to cause them to bind on the output shaft.