The output transformer has a 9V-0-9V, 2 Amps on the secondary and 230V on the primary. Use suitable heat-sinks for MOSFETs. Remember that this is not a sine-wave inverter, not even a modified one.

Alternatively, you can add gates to the drive circuit to turn off both FETs whenever the battery voltages balance. The minimum input voltage is a function of the gate thresholds of the FETs. The ±9V ...