Intermediate Cranking

With the problem described in post #6, you would still get a 'click' sound from the solenoid operating.
It could be n/switch, relay or wiring.
[1] Relay is easy to access, so I would try replacing that first.
[2] Problem remains. Piggy back a 4 ft length of wire onto the n/switch terminal. Strip 1/4" insulation off the other end of the cable & insulate it. Next time it happens, grd the bare wire. If it starts faulty sw.