House battery problem - is it me or Interstate?

As others have said, the 13.4v charging voltage is a problem. A modern converter charges at 14.4v, or more, for several hours before dropping to a lower voltage.

You may also need larger wire between the converter and the batteries. Your batteries could draw 50-60a at 14.4v when discharged and the voltage drop in the existing wire, depending on it's size and length, could be considerable thus reducing the charging current and increasing the charging time.