As I see it, you have a couple of options: (1) just get a new wiring harness and be done with it, or (2) you probably could replace the burned sections of wire. Use the same gauge of wire, solder it and use shrink-wrap on the connections. Since it will be under a wrapping tape, the insulation color doesn't matter. More work, less money, and you keep the original stuff.
I know, it looks daunting, but replace one wire a a time, so you don't get lost, and it should go well.