On the speedo cable shorting. I've heard of clutch cables doing this, but the speedo cable terminates into the dash into the back of a plastic assembly and that plastic would isolate it from electrical transmission. Imagine a metal cable terminating in the center of a small bucket's bottom and you have the visual. No metal-metal connections.
Clutch cables, or auto tranny shifter cables connect two large metal bodies and are susceptible to this issue if someone forgets to put one of the big factory ground straps on.
Also, if a cable does get in a ground path and heat up, it would show damage along its full length. As this appears confined to the area where it's closest to the hot exhaust pipe, I think it's safe to assume the missing heat shield is the culprit.