Is the wire from your ignition switch to the solenoid the original one? I've had the same problem with several GTO's in the past, and the final fix, after trying EVERYTHING else, was to replace that wire. It degrades over time, and when hot, gets super high resistance. Am running stock GM starters in both GTO's, and they've been in there for decades with no issues. And it gets HOT where I live. It only took me about 20 years to figure out the problem with my '67, and after the wire replacement, no issues at all.
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Jeff 
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