[GreenWater]

I am thinking you have a serious squeaky hatch problem. ha ha Just kidding.

Could there be a problem with the transmission? This maybe a stretch, but how about a gear that is severely worn. I am thinking of the ring and pinion gears. If they are worn bady and under normal power they are not slipping but under enough power the gears are not properly seating into each other and are kind of jumping around making the shaking in the car and also causing the shaking in the shifter. Just me imagining out loud.