Normally a surge protector (ie EMS) detects incoming AC from the pedestal and an open neutral is a pedestal or wiring problem to the EMS. So not understanding how a down stream inverter is involved when the EMS says open neutral?
Some inverters have an internal automatic transfer switch (ATS) and pass incoming AC to the output when the inverter is off. When the inverter is on the inverter (from 12V) produces AC output and bonds the ground and neutral. This could be your problem.
With the inverter on what is the 12V DC value at the inverter input terminals as measured with a digital voltmeter when the output is 100VAC?