Would it be better to use spaghetti tubing (or heat shrink, whichever listed for the purpose) to slip over the damaged portion of the insulation on the existing conductor? (remove the crumbled or scotched insulation, and use the spaghetti tubing as new insulation, and overlap the tubing over existing good insulation). That way, there's no splice in the copper itself. You could use spaghetti that has a higher temperature rating.
