Disagree all you like but if you knew anything about balancing you'd know why 4 cylinders vibrate more than others. All the other cars with 4 cyl were either RWD (2 opposing 90 degree rubber mounts, one on each side of motor) or if FWD, had 4 point mount (or more) which stops it much better than 3 point mount which Focus has. One of Ford's mistakes. Quite literally there is nothing on the engine itself to restrict the motor moving front or rear, the damping is mostly up and down. The secondary vibration of a four is partially front/rear, once the hydro mount loosens up it does not damp that out any more as it barely did even when mount was new. In fact, once mount is dead it does not dampen in the up direction much either, only down. The reason for the 'Focus shake'.
While anything is possible, it would be extremely unusual for the transmission to cause it. If trans is working correctly other than that complaint, it will most likely be a mistake insisting that someone pull or disassemble trans to stop vibration on these cars. There is simply no up/down or side to side moment to make vibration in trans, it all rotates.
First part you should be looking at is the passenger side engine mount, that's where most of it comes from although others can contribute.