There may be an easier way...if you are an EE
I have been working with a leading robotics firm, and we have been toying with high torque DC brushless pancake motors. They are small enough that you could stuff them into the wheels of a MINI, and power them from some sort of internal battery bank. Using a good planetary gearbox and a custom hub, you could power the rear wheels directly... Or you could stuff it into the battery compartment area, and use small stub shafts to power them together...
It wouldn't be true 4WD, but it would be ON-Demand 4WD. With some electronics and some good electrical engineering you could basically make a hybrid electric 4WD system.
Mitsubishi's new concept car (supposedly a replacement for the Eclipse) uses a similar system, they call it E-boost.
It is probably the best system in a car as small as the MINI...no driveshaft to bother the floorpan, just wires.
Drive Fast! Drive Sideways!