I would recommend against a wire nut here. Getting six or so wires simultaneously well-connected in a wire nut is not as easy as it looks, and they can sometimes work lose in high vibration environments (especially if not taped to prevent unscrewing).
Replacement bus bars and their mounting brackets should be available (they're more or less standard parts, even if not specifically designed for this particular electrical distribution panel); put one in, trim back the burnt/discolored portions of the wires, and attach the good parts firmly and properly to a new bus bar. If the wires are too short for this, you'll have to do some more extensive rework--maybe as simple as removing some slack from behind the electric panel.