I may have not described things very well, so I'll try again. When I begin from a stop, either reverse or forward, and put some revs in the accel. pedal & just begin feathering the clutch out toward half way (not all the way out), so that the clutch is not fully engaged yet, it will begin a violent shudder/shaking of the whole car. Of course nothing like this happens when the flywheel is engaged with the driveline & the car is moving down the road at speed. Only at the beginning.
Best example, if you were in the Seattle freeway stop n'go traffic, & were continually breaking & clutching again to get the car moving by just feathering the clutch about 1/4th, it will shudder each time.

I'm just at a kind of head scratching mystery here.