I have a friend with the same (new) T5Z transmission conversion in his '66 as I have in my '66 Shelby. Centerforce clutch assy, new U-joints (I believe) and driveshaft. His car performs flawlessly at any speed forward, but shakes voilently what starting off from a stop in reverse, especially noticable if trying to go up a slight incline in reverse.
Thanks guys. I thought about the mounts. Looked under the car and the motor mounts 'look' fine. I didn;t see any signs of seperation. The motor does not have any excess movement when the throttle is winged, unless the mount under compression is broken. I didn't check his trans mount. I would guess that it would be new. Rear springs look ok. It's definately pretty violent, especially backing up a slight incline. I was also thinking U-joints.
I had a work pickup that started doing the exact same thing - as a matter of fact, it got to the point that I could not even back up any type of incline. I had to take the truck in and the transmission was adjusted. I think some of the bands were out of adjustment. Fortunately the truck was under warranty, so I have no idea of costs.
You might check with a reputable transmission shop.