Engine/drivetrain vibration?

Did the shop have the vibration damper when they balanced it? Was it internally balanced or balanced taking the '73 340 damper and torque converter weights into account? You need to find out what the engine shop did to balance it.

If it was balanced "externally" like a stock '73 340 then get the B&M flex plate for you application and run your torque converter with no weights. That way you'll never have to worry about having weights on your torque converter.