If it ends up being a starter not engaging problem, here are things to fix it.
GM heavy duty " heat soak" solenoid sspring, a solenoid shield or maybe a starter and solenoid shield, a high amp battery. Make sure you have a good high torque starter.
Sounds like there may be other problems with your GP but the above is steps to prevent the starting problem due to solenoid getting too hot.
Good Luck.
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