You need to put the voltmeter at the converter's output terminals, or at least at the DC fuse panel lugs where the converter is connected, and look for 13.6 volts. (BTW not "current" it's "volts")
You appear to have a huge voltage drop from the converter to the battery wires by only seeing 12.5 volts or else the converter has an internal fault. If you find 13.6 at the converter, then you know it is ok and now the task is to find the mystery load (loose wire connection, loose fuse in its holder, rusted frame connection, whatever)
The fridge needs "12v" to run on 120v, so the converter is supplying that, even if only 12.5v.
The batteries run the 12v things ok, so the path from them to the DC fuse panel is ok. If the converter does 13.6 then it seems the fault is between the converter and the DC fuse panel. Tighten the set screw lugs where the converter's wires go on the DC fuse panel (might be on the back of the panel for one of them)
