Harmonic balancer?

OK, you can confirm the crank casting PN from this list to see if it is forged or cast:
The Mopar 340 V8 high performance engines

With the heavy rods and pistons that all sound like stock, then if the crank is cast, then it would be hard to internal balance unless metal was added to the crank throws. You would see this on the biggest throws at front an rear. But this is all circumstantial info; again, if you can get any info from the machine shop or the seller, that would be good. Otherwise, the best guess if the crank is cast is that you are going to need the 340 cast crank specific damper.

How about looking at the flexplate and TC next to look for imbalance?