1968 340 harmonic balancer and main pulley

As said above, the wobble can be just due to the age of the damper/balancer. There is a thin rubber between the inner hub and the outer ring of the damper that gets old hard, rotten, and cracked. It could allow the ring to slip out of alignment. Being this old, it is well past due for replacement anyway. Once the rubber gets hard, it does not do its job right anymore, and if the rubber is cracked, it is even worse. And if the rings flies off due to the rubber failing, then all he** can break loose.

As TMM says above, the 360 balancer is not to be used on the early or late 340's. You need to have the right one to avoid excess bearing wear, and other possible problems. Just because it has been in there for 2 years does not mean it is right.

If this is a 360 balancer, it will look imbalanced. It would look like in this thread:
But, we need to ask another question: Was this engine rebuilt, and if so, was the engine re-balanced, and if it was re-balanced, was this damper provided to the machine shop for the re-balance process?

If the 340 was installed, and the old 360 damper just put on to complete the installation, then it is 99% probable to be wrong.

And yes, the pre-1970 timing marks were on the passenger side of the timing cover. 360 damper marks would be set up for the cover's timing marks to be on the driver's side.

Of course, now we need to ask the questions about the flexplate and torque converter, of whether they came with the old 360 motor? The same 340 to 360 balance differences existed at the back end of the engine.

Sorry to be so confusing.....