Balance Problems...Vibration......

What year is the 340? And is it a cast crank or steel? If it's a cast crank then you should have a offset weight built into the dampner and a weighted converter, if not then you will need a B&M flywheel, as most aftermarket converters don't have the weights on them. And this is what it sounds like to me that the crank is cast and the converter needs to have a weight on it, but the simplest sloution is to put in the B&M flywheel as it's SFI approved and stronger than the stock one. They run about $70.00 from summit. If the B&M flywheel doesnt do it then the engine will have to come apart, it's the only way.
Also professional products sells the best dampner for the Mopars, as you can use it with either the cast or forged cranks as they have a removeable weight, and they are one of the cheapest ones out and look very good, you can put the weight in a couple of different spots if need be.