I just reread the post start to finish. You had no vibration with the old flywheel but now you have a vibration with the new one. With the clutch in the trans should be decoupled.
I think your new flywheel is the culprit.

When you get to the point of tearing it apart again get it in the "engine only configuration" with the new flywheel. Check for vibration.
If its OK add the clutch and check again.