I had a similar problem many years ago. I would get a almost violent shaking from a stop that I could feel in the steering wheel. The clutch wore out and I had it replaced, still experienced the shutter and quickly wore out the new clutch. Figuring I could screw it up cheaper myself and maybe I could actually fix it, I did the next one myself. Long story short, I also replaced the clutch throw-out fork and the pivot piece, that resolved the problem. Being young and inexperienced I didn't take notice if the flywheel was burned or not but the problem was gone.
By the way it was a 1968 C code fastback, 4 speed, manual steering and air conditioning. Who would order it that way?