Had a similar problem with a 68 Mustang. Did it all -- balanced all 4 wheels; new u-joints; balanced drive shaft; even swapped out the rear center section and checked the axles and pinion angle. Then I had the rear wheels balanced on the car and the tech advised that it must still be a driveline problem because he got the same vibration on testing each side of the rear (causing me to go even further up the line and suspect the trans or torque converter). But I ultimately determined that the problem was that both rear sides were out of balance not in the wheels, but the drums. Seems I did a rear brake job that required new drums, and both of the new drums were unbalanced. Since both sides were unbalanced, the tech checking on-car wheel balance assumed it must be originating up the driveline instead of thinking it could be an imbalance on both sides of the axle at the same time. A pair of $10 junkyard drums solved the problem -- after spending untold time and money, and just before I sold the car.......... You didn't have your drums replaced recently, did you?
