I thought maybe you may have a post 72 340 with pre 72 flywheel etc, but since your vibration issue appears only under hard acceleration, engine balance is not an issue IMO. I would suggest (same as above) checking the drive line components and motor mounts (transmission). Trying to find a load related dynamic vibration can be tough but there are several checks you can make with the car at rest. Some examples:
-Pinion angle in relation to the drive shaft. It should be about 2 degrees NOSE DOWN at rest, definitely not NOSE UP.
-Cracked leaf spring(s).
-Worn leaf spring bushings
-Cord separation on the rear tire(s)
-Worn U joint(s)
-Bent/damaged drive shaft
It should be pretty obvious when you find it I think. Post back your findings and good luck!