Shake rattle and roll
The Machine shop I prefer to use only balances an engine with the balancer and the flywheel/ torque converter. It sucks because if you want a different stall speed.
Rebalance. Last one done the owner used my specs on file and balanced it for the engine. I thought zero was zero. But it made a difference.
I never knew you could buy a 360 from a big rebuilder neutral balanced.