Dave, have you tried changing the settings for low voltage transfer?
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From the manual:
Low AC Transfer(V):
This is the voltage below which the unit will no longer recognize AC as “good”,will open the relay, and will attempt to transfer to Invert mode if Invert is Enabled. The range of values is 85–110Vac.
Low AC Transfer (Hz)
This the frequency at which the unit will no longer recognize AC as “good” and will attempt to transfer to Invert mode. The range is 40–59Hz.
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Try setting these to the lowest values. When the A/C starts it will draw in excess of 30 amps for a very short time which pulls down the generator voltage and slow down the motor (hertz). Setting the values to minimum might allow time for it to recover without switching the inverter auto transfer switch.