This happened to me last summer on my 67, using a new, genuine Ford Service part...two different ones. The first one cooked the wiring back to inside the car, including the loop wire in the Tilt-Away's starter disable adapter harness.
My theory differs than yours...I theorize the solenoid's "I"post (inside the solenoid) welds itself to the post going down to the starter, thus trying to RUN THE STARTER MOTOR using just the 18 ga. wire!
