Get out the voltmeter and verify the situation.
Put the meter right on the inverter input terminals, note how much the voltage drops when inverter starts running. Do the same right on the battery terminals. Post the results.
Depending on the situation move the meter to detect at different places to verify connections are good.
Not sure how far the pairs are apart but this could be the issue. The near pair is probably over worked. May need to wire the near pair in parallel and then connect in series with the second pair also in parallel. The full series connection should be 2/0.
If the wiring is not changed, the close pair will be overworked even if the inverter-microwave resolves the issue with lower amps draw.