Heat Soak Mini Starter

"There is a way" around the Ford solenoid / neutral safety problem. In the late 70's Jeep / AMC used a Ferd solenoid look-alike which had one extra small terminal. That makes a total of ......2 large and 3 small terminals. The added terminal goes to ground through the stock Mopar NSS

I would do some voltage tests. Measure voltage RIGHT AT the starter when cranking, first when cold, and then when trouble appears. You want at least 10.5V, the more the better. Then measure voltage right at the battery and compare readings. The less difference the better