69 Barracuda Clutch Shake Help Needed.

Does your diff have a snubber on it. If so, measure distance between snubber and vehicle floor, cut 2x4 a little longer. Jack up rear, place 2x4 between floor and diff snubber, lower jack trapping the 2x4, thus stabilizing diff , drive it.
All diff motion has been cancelled and shake will likely still be there.

I would also chain down the driver's side of the engine to limit engine lift, and subsequent clutch linkage motion.

RE-Resurface flywheel. jmo