I have the same problem on my SC400. Bottom line on my car the drive line was the problem. on the Sc400 the drive lined is mounted via two rubber discs. one of my discs was damaged which cause the vibration when ever it was under prower, but would not be there when coasting.
the various parts are expensive, my solution was to replace the entire drive line, expensive but it worked. You or your dealer can do the inspection - good luck