You probably know that the two house batts should be "deep cycle" and a reasonably matched pair for model and age. Possible you need to buy a matching batt like the one you just got assuming you got a deep cycle one.
Is the power centre 50 amp? You said half the lights quit in the OP, so one leg and the other leg ok? I have no clue about how the legs thing works with 50 amp so somebody else will have to help with that. Just setting the scene here if that affects your mystery voltage readings.
Good news that the converter DC terminals can be read vs at the fuse panel.