When you checked those voltages, how heavily were you drawing on the inverter. If a lot of load then the converter was putting out a lot of amps and there was a significant voltage drop between the converter and the batteries.
That is one of the common flaws with RV converter installations, they skimp on wire size, maybe as small as 8 gauge. If the inverter is drawing 50 amps to satisfy a 500 watt AC load then the voltage drop could easily be 0.6 volts if the distance from the converter is 8 feet or if the current is 25 amps and the distance is 16 feet.
Or there could be a bad connection that is causing a large voltage drop. Feel each connection and if hot tighten them up.
David
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