In addition to what Schmidtys suggested, do you have a good digital volt/ohm meter and have you checked the voltage at the relays and at the starter when you push the start button? You could have a problem in a cable somewhere, not just at the connections, that is causing the voltage to drop where the starter puts a load on the cable. i would sure check everything possible before laying out the bucks and labor to put in a new starter and maybe find out it doesn't solve the problem.
Maybe try connecting the Jumper cables from your car with the motor running directly to the terminals on the starter motor and see if it still doesn't work.
1987 Softail Custom, stock except for added chrome, and still running like new after 100,000 miles.