Had the same complaint on the Truck and a 48 Sedan. What was common to both? One driver side motor mount. Truck had a bolt missing to the cross member. Car had a mount missing the rubber and both failed to control the "torque shift" when just engaging the clutch. The bolt was easy. The mount was a PITA. 2 bolts to the bell housing and not much room to get at them. And so much crud from the pedal pivot shaft and the dirt from the road. But still less work than pulling the transmission. Now both are smooth and stable. Easy to check, put a jack and a wood block at the rear of the oil pan. Lift and observe. If the motor lifts off the cross member, the mount needs attention. If it stays put, look for oil on the fly wheel. Take care to NOT bend the pan.
