I think the factory is dead on. Find the little (silver) CB.
Since your voltage is staying rather steady at the battery and you are completely losing it at your devices there certainly is something in the line that is opening.
I had one buried deep inside an electrical box on a previous RV. Could not bring the slide in. Brand new rv too. Luckily I had my handy voltmeter and with brute strength and ignorance I sorted it out.
You basically need to follow every inch either from your battery or from one of the devices back. However with multiple devices they all should lead back to some sort of fuse panel. At the fuse panel you probably have two input sources, one from your Converter (which does not exhibit the problem when connected to shoreline), and your battery input wire.
Can you find a schematic for your rv?