Gate drive transformer for lower frequency (25 kHz)
This is just my thought experiment.
Since Arc Impedance is a low negative resistance (NR), the maximum power (MPT) will be transferred when the arc impedance matches the power supply impedance, but that also means 50% loss so that may not be ideal.  It may be a conjugate capacitive conductance of current with a reactor inductive source to make it less lossy.
The conduction voltage also matches the arc path length.  The higher the current density of the arc, the lower the (negative) impedance of the arc.  This is critical in designing an efficient power transfer for a 1kW arc welder or in this case an Ozone generator for non-occupants.
The ionization or Breakdown Voltage (BDV) is much higher than the arc voltage, Varc and also the impedance ratios are mismatched for an HV source to an arc load, so a dual-source approach must be considered.
This could be the parallel inductive coupling of your 300V DC source with a 20kV spark generator just to ignite the arc but not sustain the high current of &gt; 3A.
By raising the arc length the voltage may be increased.
Without design parameters, I cannot go any further but the output inductors must be chosen to sustain the current without saturation with significant RF resonance and arc noise which may enter the microwave band depending on the arc path wavelength and harmonics.  It seems the Caps from the HV inductor create a high-frequency Relaxation Oscillator.
Here's another approach using a Tesla design with dual transformers and a long high impedance arc with an intermediate Relaxation Gen. using a 3kV spark plug ~ 1.5mm.