Also, does it make sense to model the spark gap as a 1+ meg resistor?
A spark gap resembles a neon bulb, except its threshold is more like 1,000 V rather than 70 V.
I know of a simulator which contains a model of a spark gap. It's at falstad.com. It's animated and interactive both.
CLick the link below to open the website and load the spark gap simulation (Sawtooth generator). CLick Allow to load the Java applet. It will run on your computer.
The Circuits menu has a couple more spark gap simulations (Tesla coil, Marx generator).
You can alter the circuit by right-clicking on components to bring up an edit window.
https://tinyurl.com/8f63dft
I don't know if you'll want to re-do your entire schematic in Falstad's simulator, however.
Would you happen to have any comments on the values chosen for the transformers? I've read that you can simply take the turns ratio and square it for the inductance ratio to simulate, but in some cases the difference in magnitudes seem absurd.
When you send DC pulses through a transformer, things are not as straightforward as with AC sinewaves.
For your frequency of operation there ought to be a henry value which is most efficient at transferring power from the primary to the secondary.
Use too high a henry value and the result is that primary current is slow to build during On-time. The flux field is weak. The secondary has weak response.
Use too low a henry value and you have start getting inductive saturation during On-time. The flux field becomes stationary. The secondary becomes idle.
Guess it turns out to be a process of trial and error.