I bet the driveshaft is whipping around in a bad rear bushing, and the rear mount is sending that vibration straight into the chassis. I wonder if your driveshaft is too short. If so, you will need to fix that or it's gonna happen again.
When I wiggle the output shaft the input flops around like a joystick. The driveshaft is 50 inches long from knuckle to knuckle and the extension is 9 1/2 inches knuckle to end. Installed it looks normal to me, a couple inches of silver showing. 59 total.