I believe that the governor controller can be adjusted on that machine, will need the laptop, software and cable.
Yes, possibly harmonics doing this.
Try adding a resistive load such as a heater, a 1500 watt would be good and then turning on the charger. If it helps/cures the problem,time to call Onan, this time go to the factory instead of the local dealer for resolution.
Point out to Onan that another brand of generator works OK, why does theirs have a problem?
If I can't fix it, it ain't broke.