Produce a low voltage DC (i.e. one that is isolated from the mains AC side) and then design an oscillator that produces 300kHz and runs from the DC supply created.
If you produce a 15V DC supply and you make an oscillator with the induction coil in the collector of the power transistor you'll be able to get 24V pk-pk no problem. Life is made easier if you resonate the coil with a capacitor. You'll probably only need a few volts pk-pk if you resonate this way.
So, basically the "frequency changer" is conversion to DC then create 300kHz from scratch using an oscillator.