'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

Here ya go