Engine/drivetrain vibration?

If all of the weight was removed from the converter, you went too far., A cast crank 340 should have a "For Cast Crank 340 Only", or something to that effect, cast into the correct balancer counterweight. The converter should still have a smaller weight than what a 360 takes. If the converter is now neutral and it IS a cast crank, get a B&M flexplate for a cast crank 340 to balance it out.

The forged 340 crank takes a flat balancer/damper, like a 318, and a neutral balanced converter.

Did you change any internal parts during the rebuild? Pistons, rods, etc? That would likely require rebalancing the rotating assembly.