Perhaps we could add a psuedo electronics and AVR section to this forum?
In pre electronic times, like 200 years ago when I was a boy, voltage regulation was done passively, and did work rather well. I remember the old Westinghouse, Vickers, Markon stuff that wouldnt know what a transistor or SCR was, yet they ran well and maintained pretty good regulation and certainly didnt flicker.
Easier than messing with heavy flywheels, try this.
Magnetic amplifiers were common back then, although they were not recognised as such at the time.
Its easy to make one.
take a common isolation transformer.
Short circuit the output terminals, or the input, it wont matter.
The other two unshorted terminals are connected in series with the generator load , ie the IT live goes to the live of the generator, the neutral to the lights/house.
What this does is place a current sensitive variable inductance in series with the output generator current, the current increases as the voltage increases on each mains cycle, therefore filtering occurs on a cycle by cycle basis , much more accurate and quicker than can be achieved by varying exciter current alone.
A transformer "reflects" the impedance from the primary into the secondary, therefore with light loads, the transformer will have a higher series AC impedance than with heavy loads ,this is dependent on your particular core saturation curve, reluctance and other boring stuff
Given the random nature of your transformer and generator combo, this may work well or provide no change at all., but is just minutes to try.
Ideally, custom inductors are required, but luck can happen with commonly available items.
I am assuming those with the nounce to be messing with this stuff also know to be safe.
To have this work well, a low value high current wire wound type adjustable resistance load should replace the transformer short, and then adjusted for best performance. These will commonly be in around the 5 to 25 ohm range allowing the core saturation level to be adjusted
This method can remove all high frequency flicker and tidy up shitty waveforms. when set up correctly
The transformer VA rating needs to be at least equal to the average generator load, err on the heavy side, if unsure, watch the temperature rise, warm is ok..