If you wire a remote solenoid it will bypass the one on the starter.
Sorry Dennis, but that isn't the case. A remote solenoid simply provides low resistance batt voltage to the GM solenoid's "S" terminal. The GM solenoid still needs to be in good condition as it moves the pinion to the flywheel and provides the contacts for the motor to spin.
Kevin, try this. When the motor is hot and won't start with the key, connect a remote starter button button between the batt post on the solenoid and the S terminal. (not a screwdriver) If the motor cranks normally, you can rule out the starter or the solenoid. The problem will likely be in the harness "somewhere". My guess is that it will crank, but if you still get nothing, then the problem is with the solenoid.
You can also put a voltmeter on the "S" terminal and have someone turn the key. If you don't even get a click out of the solenoid, you will likely see way less than 12 volts, perhaps even 0.
When you rewired the car did you replace the ignition switch? If not, it is a likely culprit. Each time it is used, it creates a small arc which over time pits and corrodes the contacts, increasing resistance to the point where it can't overcome the naturally increased resistance in the hot solenoid.
If you decide to go remote solenoid, I recommend a 50a Bosch type relay instead. It's a cleaner looking install, and provides low resistance batt voltage to the S terminal, which is the goal.
Wiring as follows: (12ga)
85 - ground
86 - purple "S" wire in existing harness
30 - battery terminal on solenoid
87 - "S" terminal on solenoid
87a - not used