The capacitor in the genny is used to provide the excitation to the field exciter coil.
The field coil then excites the armature/rotor, which has coils on it that respond to this field. The rotor coils have a diode across their output, and so makes the rotor current DC........so the rotor becomes a big bar magnet spinning inside the stator.
The power windings in the stator ( separate from the exciter ones) then feed the 240vac output, and it all self regulates..... good times....
But...If we decrease the cap value, the voltage on the output drops, if we increase the capacitance, the output voltage rises ( frequency stays the same from the governor). So by adding even series capacitance on the output, we alter the relationship in the tank circuit ( resonant circuit) of the exciter /capacitor, and the voltage will skyrocket with the addition of the "softening " caps we try to add. This will blow the GTI filter electrolytics to hell and back... within a few seconds probably.... so no we can't use that technique with that style of genny.
If you have nice little genny, direct rectification will work, but the mppt of the GTI will cause it to hunt, as the mppt tries to fuzzy logic the input. As it gyrates around the best settings it can find, it necessarily tests the waters all the time... continuously, so changes the loading all the time.
If the genny has stamina, it may not change rpm too much, and won't cause much concern at all, if it is a bit soft, it may be like the tail wagging the dog sort of thing. The series caps gave the mppt a higher impedance source, so it could see the voltage sag, as it tried too hard, and come back as it eased up a bit. This gives the mppt something to work with...... but the cap excited genny........ no.
Direct connection via diodes will probably not cause the high voltage problem, as the GTI filter caps are after the diodes... but no idea how the hunting will effect the outcome. The fact that you can use a inverter welder on your genny, is a fair indication that the filter caps after the diodes won't cause a voltage problem, as the inverter welder has diodes, then caps..... essentially the same thing as the GTI front end with diode bridge ahead of it.
I may do the induction motor thing soon as well for another site here with different circumstances... we'll see. But it will need a control system to allow for a novice to use it, and just let the genny run out of fuel..... and unless you want the inverter to drive the petrol motor after it has run out of fuel.... this will be a problem for them..... ie only allow the motor to connect at 50hz or more, never less.... ie 3000rpm or 1500rpm motor dependent.
I'm not an expert in any way.... just good at blowing things up.. then having to fix them
............oztules