Engine was rebuilt.
New pistons?
New pistons with weights very similar to OE pistons?

I can add that, 30 years ago I built a 360 with trw forged replacement pistons. Weights very close to stock.
I used the B&M flex plate, and balanced it myself.

It needed more weight on the rear than what the flex plate provided.
I ended up adding three fairly large holes to the flexplate to increase the amount of imbalance to get the crank to balance out.

The front, which had the factory balancer, was fine.