1969 Valiant, 340...TCI 727...8 3/4 w/3.55
The vibration is because of the pinion angle and trans are not in proper alignment. I'll bet a 12pac of Stella that it's off. My 68 had the same problem after I lowered the rear end with new springs. At first I thought the trans mount (727) was too tall.
I then discovered the pinion angle was off by 3-4 degrees.
Remedy degree shims for the rear to correct pinion angle. Shims can be had at any 4 wheel drive repair shop.
Send the beer to my work...