The prototype push charger is now complete. Starting where I left off on the disassembled remote-control car, I added a diode bridge between the wires coming from the gearhead motor and the battery compartment. The diode bridge ensures that the battery always receives the same polarity of current. Even if the push charger is being pulled backwards, voltage will always flow in the same direction.
Completed push charger, with diode bridge covered by insulating shrink-wrap:
Pushing sticks made from reused bamboo, attached to the push charger: