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

Oldmanmopar said
Does this happen when pulling out around a turn or going straight? Around a turn it could be the clutches in the sure grip which is normal. Just let the clutch fly and drift the turn you won't hear any noises.

You mentioned it has a diaphragm clutch. Is the large overcenter spring still on the peddle assembly under the dash? It shouldn't be. A diaphragm plate does not need a over center spring. It will be noticable on the engagement on a RPM shift or pulling out .

Now that you mention it, it may be happening more on turns, but I would swear it has also happened on a straight away. I will pay more attention going forward and try what you suggested. I looked at the clutch pedal and could not see anything that looks like a spring on the mechanism.