How about checking / cleaning the grounding strap and connections?

Somehow the voltage / power to the solenoid via the key switch is not sufficient, or the solenoid is weak (yes I saw that you replace the starter, if a rebuilt starter then it still may have a weak solenoid if that was not renewed). You could hook up a volt meter to the connection at the solenoid and see how much voltage is reaching the solenoid during the "no start" condition, then work backwards on that circuit to see where the voltage drop is happening.

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Respectfully,
/s/
M. Dillon
'87 124.193 (300TD) "White Whale", ~392k miles, 3.5l IP fitted
'95 124.131 (E300) "Sapphire", 380k miles
'73 Balboa 20 "Sanctification"
Charleston SC