'67 Barracuda Fastback S 383 4 speed rear end issue?

New owner here, and my questions are piling up. My noob status is quickly becoming apparent, so sorry for that. I think I may have an intermittent problem with the 3.23 sure grip rear end, but I'm not sure, so...

According to the previous owner, the car has a new McLeod diaphragm style clutch & throw-out bearing, flywheel was resurfaced, clutch linkage was rebuilt, and shifter was upgraded to a Hurst Competition plus conversion from the original inland shifter mechanism, so I'm assuming it is not a clutch issue. I am not aware of any work done to the rear end, so I'm assuming that is original and 53 years old. Here is the symptom as best I can describe it...

It happened a couple of times on the test drive, and I assumed it was just my inexperience with driving it, but now I am questioning that. When starting from a dead stop in first gear, I get what I can only describe as a severe shuddering of the rear end. It feels like the tires are wanting to spin, but they won't let go and the whole car shakes until i disengage the clutch, give it more throttle, and slowly re-engage the clutch (sometimes a few times) until I get it going smoothly.

After buying the car and getting a better feel for driving it (I have had it a week), I went a while without a problem, but now it seems to be happening again intermittently. I swear the clutch action feels different when it happens, and I don't think it's me. The clutch action feels 'normal' most of the time and I don't have issues up shifting or down shifting gears 2, 3, or 4. Does this sound like a problem with the drive train or the driver? I have as of yet not intentionally tried to do a burn out. I have been in 'baby it' mode for the most part up to this point. Any sage advice to an admitted greenhorn would be most appreciated. Thanks
Sounds to me as if the clutch is giving you the problem. You could elevate the rear of the car and do some basic investigation.