I have the lowly 300 so my only experience with severe engine shaking...the kind that made the whole car feel like it was bucking and about to explode...was due to the ignition wiring harness shorting into the engine block...you could see the current (blue) jump into the block when the car was running. It wouldn't move and it was rather scary. Your car doesn't have the harness issue, but it could be something shorting in the cap etc...only a guess. Best of luck with it.

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2004 Chrysler Crossfire