Square wave inverter
Yes, at this input voltage a center tapped primary with low side switches on the ends seems like the way to go.  For feedback, I'd look at opto-isolators first.  Put something on the output side that can detect whether the voltage is above or below the regulation threshold and drive the opto accordingly.  On the primary side, a simple control method is to simply stop the oscillations when the opto signal indicates the output is high.  If you can live with some ripple, this should be effective, simple, and efficient.