you lost me with this line lol, you ain't doing a god damn thing fast in a 720! As for the bucking under hard acceleration, try changing the fuel filter. A clogged fuel filter will first causing issues when the engine needs the most fuel like hard accelerating or pulling a hill.
As for the shifter moving when on and off the gas, I would have someone get in the truck and rev it up and down while you watch the engine. Maybe the motor mounts are trash and everything is shifting?