It's got to be the balance. What else could it be?
That is why you using the complete 360 with balancer and flywheel would have eliminated that part of the equation. I wouldn't have guessed that the flywheel was a different size and the clutch wouldn't fit it.
Since you are now an expert at R&Ring the trans, you can try installing the big flywheel and big bell housing, without the clutch installed, throw on the tranny for the rear mount, install the starter and start it up. Factory balanced engine and you can rev it up to see if the vibration is still there. It never vibrated in the truck, did it?
One thought crossed my mind though. I've had my car for so long that I can feel a miss if one plug wire falls off. It doesn't pop or backfire but vibrates a little. Are you using the same plug wires from your 340 on the 360?