Check the inside of the ball housing for scoring or dings in the metal. A u-joint that flops around will hit it as it turns. For the most part these marks can be smoothed with some emery cloth and elbow grease. If the bushing in the torque tube is worn this might cause vibration. A worn bushing could also lead to seal failure letting all of your trans fluid leak to the differential.
This happened to my 49 and I put the Okie system in. Not really a very hard job. The most difficult part was removing the old bushing using my primitive methods.

1949 Chevy 1/2-Ton
"Sedgewick"
In the Gallery
1989 Caprice