I don't get why you would want to put an extra gear ratio between your motor and transmission. You already have a box full of ratios in the transmission and then another ratio in the final drive.
Electric motors are usually at their most efficient when they are close to their maximum speed. At that point the the back EMF opposes the current flowing in and reduces the current right down until there is only enough to keep the car rolling. The amount would depend on the resistance the car experiences at the time.
So, on the flat at x mph there is a combination of air and rolling resistance. That takes a certain amount of torque to overcome. If the motor was spinning fast and the producing only enough torque to keep the car moving then it will be using the least amount of energy to keep going.
It is the opposite of an ICE. In the ICE you would want the RPM as low as possible and still have the torque to keep the car running. With electric you want the motor rpm as fast as it is safe to run at and still move the car.
So, that means for your average car you may do most of your driving in 2nd gear and then using 3rd to reach freeway speeds.
You would figure the highest safe speed for your motor and the road speed you want to cruise at and then find the gear in the transmission that is closest to it. Changing the final drive ratio could help move those transmission ratios closer to the best point for the motor efficency.
However, all that only works well if you do a lot of steady cruising on flat roads. If you don't then you stir the transmission a bit more.
Raising or lowering the overall transmission ratios by 3:1 would either cut your top speed right down as you run out of safe RPMs or have your motor spining really slow and pulling high amps.
Ultimately, in a lossless world it wouldn't gain or lose you anything as the energy to move the car is the same whatever the stuff between the batteries and the wheels were doing.
In our imperfect lossy world you will get losses and then have more losses on top due to running higher current at low RPMs, spinning another gear set, spinning another set of bearings, stiring another quart of oil, etc.