In an effort to increase the efficiency of our Solar Charger Circuit, we decided to produce a PUSH-PULL arrangement. This involves two transistors. Each transistor is in common-emitter mode driving a 50 turn coil with the feedback coming from the opposite 50 turn winding.
If you look at the circuit you will find it is exactly the same as the Solar Charger circuit, with two transistors in mirror arrangement.
We tried the circuit and all sorts of variations but it did not work with a solar panel. It did not produce a charging current to a 12v rechargeable battery.

THIS CIRCUIT DID NOT WORK

One of the transistors was removed and we got a circuit very similar to our Solar Charger. It produce a good charging current from a 3v solar panel.

THIS CIRCUIT WORKS

Sometimes an idea will work and sometimes it doesn't. That's why electronics is so challenging.

EFFICIENCY
It is very difficult the provide any sort of efficiency with this type of circuit as it is heavily loading the panel and producing a voltage to charge a 12v battery, something that could not be done otherwise.
The solar panel we tested had a open-circuit voltage of 3.2v and this dropped to 2.4v under load.
The short-circuit current was 100mA but it delivered only 50mA to the circuit and this provided 8mA charging to the battery.
A solar panel with the same areas of cells had a terminal voltage of 22v and charged the battery at 40mA.
This proves direct-connection is much more efficient but if you don't have the number of cells to produce the "voltage-head," this project is an alternative.