anyway to control the volage level you must control the charge in primary inductance, and thats mean pwm at 50% at some frecuency with some mosfet and cheap arduino.
ATTiny85 probably cheaper than arduino

However, it doesn't matter if we use push-pull or full-wave DC-DC, but did you used FB oryginal primary windings or custom and what was switching frequency?
I have no data about this FB core ferromagnetic properties, so even if I know its dimensions, no way to calculate any flux, etc

I've added 10T as shown below on FB core and driven this thing with ~4VAC at 400kHz using low current h-bridge via 54 Ohm series resistance (2 x 27R) and 2x 100nF ceramic caps.

No sparks, so far but using my HV LEDs tester shown above it looks like pins 1-2 are shorted (no light from LEDs) and the same for 7-8, but they have resistance close to short-circuit.
LEDs had ligth maximum between pins 3-6, and the same but lower light beetween (1-2)-3 and (1-2)-6, so it looks like it might FB primary coils.
NOTE: I've connected now this "HV tester" to my full-wave ~4VAC "SMPS" directly (2x27R and 2x100nF) in series and... of course those LEDs @ 400kHz are not

burned, so a very little input current it is-theya not even bright-similar light was on FB primary coil

The only way to get any light between main red thick HV wire (0) were between (1-2) pins and light was significant low (probably less than 1mA equivalent-no supprise if there were 1:100 or more ratio between my 10T and this FB HV output coil), so it looks like pins (1-2) might be ground, while on PCB there were screws visible, however.... no sparks of course due to very limited input current and not great magnetic coupling of this added 10T to FB core

BTW: I've tested the same LEds tester with random ferrite core with similar 8T primary and ~20T secondary and LEDs output similar not too much light @ 400kHz using such current limited "SMPS", so probably will try also connect now to FB internal primary (to pins 3-6 where I've got greatest light response), but maybe someone knows those FB has splited this internal primary to be able drive it in push-pull mode during normal operation in CRT monitor/TV ?
