Hello, Here is my thinking.

First, At the common ZVS oscillator circuit, there're usually two resistors with bigger package that have around hunderds of resistance.
They, and the two of fast diodes and the resonant tank are the MOSFETs gate driving circuit. On the other hand, the two smaller ~10k resistors as the pull-down resistors, parallel to the zenor diodes (usually 12V).

So, if you increase the input voltage. This two driver resistors can pass more current for some of the more current pass through Zenor (guess 1)
And the MOSFETs gate signal is like 0V/12V (by zenor) ~square wave so the more voltage can constantly shift up Vin-12V the voltage across this two driver resistor (guess 2)
Then, I don't know for this kind of resonant circuit, if the Miller effect still plays a big part when the input power been increase (guess 3)

For your sample post SGTC. I was Lucky~ I only use a simple LCR meter to measure the L and C of primary coil, secondary coil, and primary resonant capacitors to approach the resonant frequency.

I think it is a more detailed sample way~

(1) Think of the shape of your secondary coil (it make you have to consider about the coupling), for a SGTC I think you need a longer secondary compares to DRSSTC for avoid the arc flash from the high voltage in the primary to secondary (SGTC tens of kV compares to DRSSTC hundreds V to kv).

(2) Assume the coupling factor like typical 0.1~0.3 and simulte them in SPICE to check how much inductance the primary need (The leakage inductance and capacitance make the resonant freq.)

Then make your circuit and tune them. For the resonant capacitor. I use MS15000V film-capacitor from EACO. I think CDE or WIMA or KEMET or other manufacturer are common on the market.

The current or the voltage as the leader in the primary resonant tank (Same resonant frequency, big L small C or big C small L). I don't know the actual different of their behavior to a SGTC.

By the way, https://www.youtube.com/watch?v=__IYgKmSxGM this was my goal.

That looks like within about 10% of prediction which is pretty good. Certainly close enough for initial tuning. Did you account for the tolerance of your capacitors?