First of all - I'm unsure whether you can really call the EM61 sluggish. I can reliably pull the motor into ESP, even on dry, cold roads, with stock (equivalent) tires. Sure, more grippy tires would help a lot, but what really is the value of an extra motor if the car is already at city driving speeds in about as much time as it takes you to push and then let off the throttle? How often do you really need more power? Seriously?
I've driven in eco cars a lot - the Mitsu Mirage most recently, and the Suzuki Alto before. Now those are cars that need more power. Those are cars that even with 2 people inside can't climb a steep slope at highway speeds. They're consistently slower even at maximum acceleration than anyone else pulling out from a traffic light. You're a hindrance in these cars.
The Leaf? If I floor it, I see cars standing still, quickly becoming smaller in my rear view mirror. It can climb a steep grade at highway speeds, fully loaded to 4k lbs. I just did that yesterday.
I'm aware that the EM57 (2013-17 Leaf) is quite a bit less torquey, so the 'feel' of the car may have changed a bit. Also, even though my Leaf accelerates well over three times quicker from a stop than the Mirage, the sheer lack of noise gives a false impression of slowness. Still, it's got plenty of power.
All that aside: is it possible? Yes! In fact, there is plenty of room around the rear subframe to mount a rear motor. I'm pretty sure that with a lot of dedication, you can just put a Leaf drive unit flat instead of upright under the car, and it will fit just fine. Note that there is a sea of empty space behind the rear axle. All you have to find a new place for is the electric parking brake, which arguably you should just replace with a hand-operated one if you're making the car AWD. The car also has pretty good anti-dive, decent sideways stiffness and the original drive unit comes with a differential in the package, so no need to do funny stuff to it to make it work. It won't fit stock, don't get me wrong - you'll need to make a bunch of adapter brackets to fit it to the existing suspension points and hinges, not to mention grind off a whole lot of crap, but from a volume and size perspective, this is possible.
Another update: I've driven with the car fully loaded (max. GVW) by installing a second layer of batteries AND lugging around another battery, just sitting in the car doing nothing, and a bunch of other luggage, and a girlfriend. Also, we had very cold weather (couple degrees freezing) and a 6Bft head/sidewind. Despite all that and my 12V battery dying, I managed to drive 100km with 11km on the GoM, so a decent 7-8kWh still remaining. I'm thoroughly impressed with the range now. This car only needs some aeromods and it'll be an acceptable car!