Hey...I'm the guy from for a bodies only forum. I have a '68 Barracuda 383, 4 speed, 3:23 sure grip convertible. Unlike Tim's car, my car is not numbers matching. It is an original 383, 4 speed convertible car but it was missing the big block and 4 speed and the big rear end. Anyhow, everything on my has been rebuilt or is new. Had the tranny rebuilt, got all the rest of my 4 speed stuff from Brewers. Had the 3:23 suregrip rebuilt, etc. My car acts exactly like Tim's. I originally thought the clutch was the problem and replaced it (new fly wheel). I recently filmed the rear in slow motion with my phone in my driveway and the leaf springs jump up and down pretty violently which is what the shaking is. I was about to buy new springs when I read Tim's other post and saw that he tried that and it didn't help so I don't know what to do. I put this car together myself and it's super frustrating and embarrassing that I have to take off with no acceleration until the car is rolling or it will shake pretty badly. Someone else must have had this problem before.
What you describe could be caused by clutch chatter as the assembly grabs/ slips/grabs. As the power is applied the front of the differential raises as the pinion tries to climb the ring gear. how much it raises depend on how much power is being transmitted.
In order for it to act as you describe the power has to be varying for one reason or another or the front of the springs are extremely weak. One could try an adjustable pinion snubber pre loaded to stabilize the front of the differential. Doing so would minimize /eliminate the differential movement , u joint angles changing etc. on a normal take off.
The chatter if being caused by the clutch may be being amplified by the differential movement. It would still be there but should be a lot less noticeable.
I'm still thinking something in the clutch area is at the root of the problem. Another thought that might be a possibility is a bent input shaft.
