Maybe I'm reading this wrong, but from the symptoms I understand that the high current path from the battery, through the starter relay (solenoid) to the starter sounds OK to me.
I read the fault symptom as, the starter relay control wire does not operate the starter relay. Even connecting the battery (+) directly to the control wire does not seem to operate the starter relay. This sounds impossible unless the relay control wire has no return path to the battery negative (-)... or the solenoid is just bad. If the solenoid is good then this would make it a ground problem which is a lot cheaper than a new starter.
Sorry, don't remember if the ground is made by a clamp to chassis or a separate black wire. You should be able to test this easily. Disconnect the two big high current wires, disconnect the small control wire and small (black) ground wires. Connect the control wire and ground wire directly to a battery. You should hear and feel the relay operate. Put a Multimeter in the ohm scale across the big contact posts and it should read near zero ohms. If so all is good and you only have a ground fault to solve.
Or did I miss something here?
Best of success!