Tesla initially built the Model S with one motor driving the rear wheels. The D model has a second motor driving the front wheels.
Was the increase in range and performance ... due to the ability to remove the rear drive shaft etc?
No. There was no rear drive shaft in the RWD model, the motor was installed behind the rear wheels, against the differential.
The range of the D model is about ~10 miles more than the RWD model with the same battery. I haven't found a statement that says why range has increased. One possibility is there's more scope for regeneration with the AWD model: on the RWD car, regeneration is limited by traction, most of the brake force is supplied by the front wheels.
The increased performance is thanks to the second motor.
Going from 2 to 4 motors allows you to eliminate the differentials, at a cost of having to drive each motor at a different speed, making the electronics more complex: not just the control circuitry, but you need to have two power amplifiers instead of just one.
Whether it'll improve performance depends on which motors you choose: if you replace one 100 kW motor with two 100 kW motors you get more performance but a shorter range, for instance.
An important factor is the power/weight ratio of the motors. I suspect the 2x 50 kW motors would weigh a bit more than a single 100 kW motor, as you have to duplicate some items that don't directly contribute to output power, like the commutator and the motor shaft. The 2 casings will weigh more, too. Whether the extra weight will be offset by eliminating the differential remains to be seen.