Small Vibration

Tire bulge, bad u joints, out of balance driveshaft, wrong balance on the flexplate/torque convertor ('72 340s could have been either internal or externally balanced, a 340's external balance is different than any other Mopar's external balance), or a multitude of other things...
Start with the easiest things first.
With the transmission in neutral, bring the engine up to the same rpms as it would be at 60 mph. does it have the vibration now? Yes= engine/TC imbalance, incorrect combination of parts. No= something in driveshaft on back.
Rotate your tires and see if the vibration changes. Yes= an issue with one of the wheels/tires- out of balance, sidewall bulge, belt separation, bent rim, etc. No= issue is in driveshaft or rear end.
Remove your driveshaft. Carefully check your u-joints for excessive play or looseness. U-joints can be finicky and hard to tell their actual condition sometimes. I know it's new, but consider this: I just put a new rear driveshaft in my Grand Cherokee, a custom unit that replaces the staked u-joints and CV joints with serviceable u-joints. I still had a growl and slight vibration. Long story short, I pulled it back apart and found that one of the "new" u-joints was missing about half of the needle bearings in one cup. Moral of the story is that new doesn't mean good.
Also check the shaft for evidence that it may have shed one of it's balance weights.
While the shaft is out, check your rear end pinion for slop (up and down, or in and out) or excessive play.
It's all a game of narrowing it down by process of elimination.