I experienced a situation situation similar to what you are dealing with here. Back in the early 80's my dad bought an early 70's van. It had a 360 in it and the tranny was bad. Dad put a tranny that was mated to a 318 in it. That motor always had a vibration in it like it had a dead cylinder but when you would pull the wires off one at a time they all would drop rpm about the same. This went on for over a year trying to find this " miss " in the engine. Next my grandfathers 318 in his pickup was getting tired and he had a low mile 360 out of a car to replace it. I went to this mopar guy in search of a pickup oil pan and pick up tube for the 360. He told me to make sure I change the torque converter because of the external balance of the 360. As soon as he said that I new what was wrong with dads van. We changed the converter in the van to a external balance and it ran smooth as silk.
Another example is on a one piece rear main small block chevys They are balanced externally at the flywheel. These can also be balanced internally with light weight pistons and rods etc. On a couple occasions because of miscommunication a motor has been started on the dyno with the wrong combination. When this happened it was pretty obvious as the dyno stand would shake pretty badly as soon as you raised the rpm off idle.
I'm not saying that you shouldn't try to get to the bottom of your balance situation but it might be obvious if it is the wrong balancer and flywheel when the motor is running.
I'm sure I'm not the only one to experience a mismatched flywheel and balancer. Hopefully someone else can relay their experience to help sort this out.