You got down to 12.1v "loaded" and they came back to 12.4 unloaded, which is normal.
You can still get by with the converter without the charger part working by using your battery charger as required. (The charger is not good for continuous duty at 13.6v like a converter is, it charges up the batteries and then shuts off or you unplug it.)
Or, you can by-pass the old thing and use a new converter/charger that you can mount anywhere handy. EG:
https://www.boatandrvaccessories.com/products/powermax-pm3-60lk-12-volts-60-amp-power-converter-battery-charger-w-led-light