Controlling two DC brushed motors, 12V and 2.4V, limiting current while also supplying logic circuit
Power the 12 volt motor from the 12 volt supply
Use a buck regulator to produce 2.4 volts for the smaller motor
Use a buck regulator to provide the voltage for the logic bus


That's the most likely power efficient way to do it. With 300 mA on the 2.4 volt output, the average current into the associated buck regulator will be about 70 or 80 mA from the 12 volt supply meaning you are creating more overhead current for your main motor.

Same story with the logic bus.