Scott, you mention the 'thick black cable' coming out the back of your converter. If you've determined absolutely, for sure that it is the 'shore power' wire, & if it is 'hard wired' i.e. soldered or machine 'crimped' to a lug or board, you can just connect the black (or red) wire from your shore power connector to it then wire the white (neutral) & green (ground) to the appropriate lugs as normal. I'd use an appropriate sized wire nut to connect the two, tho soldering is probably better but, if it's a # 10 or larger wire, it takes good sized soldering iron or small torch to do a proper solder job
. If you use a wire nut, leave enough length so the connection can be folded back on itself & taped securely. That should keep it from vibrating loose while being towed. At least that method has worked for me through many thousand miles of travel with various campers/trailers, etc, that I've had to re-wire or modify existing circuits