To clarify my previous post to match your remote starter relay.

Cable to starter from battery. Cable from battery pos post to relay input.
Cable from relay output to starter pos stud
Big gauge jumper from solenoid "S" terminal to solenoid batt stud
Wire to alternator from battery or relay input. Use a fusible link
Wire to ignition switch from battery relay input. Use a fusible link
Wire from relay "S" terminal to Ignition switch "S"tart terminal.


Poster calls it a "Hot Starter" issue. The remote relay trick has no small wires down to starter. Those solenoid and coil bypass wires get radiation from motor and exhaust heat. Sometimes the wires get so hot that resistance is too high and starting is hard till they cool. A form of heat soak. Also the insulation gets hardened/browned on some vehicles. Anyway, I do this all the time. The solenoid and the starter get heat soaked also/more so. This big jumper from the big cable can overcome the internal resistance and force starter to spin in some cases. I guess a shield helps also. Especially for headers.
The up-top inner fender mounted relay is pretty nice to trouble shoot and has good "hot wire"/remote start button access. I make the jumper from small flattened copper pipe and drill two holes.
The "I" terminal on the relay gives you the "R" to coil + bypass circuit if you need it. I gave the relay part numbers in pic.

Don't know if poster did this, but this is the method.
Attachments
Ford starter relay trick.gif (9.74 KB, 135 downloads)
solenoid jumper.png (23.31 KB, 115 downloads)
000_0002.JPG (403.35 KB, 112 downloads)


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