Charging system and other wiring change help needed

Depends on what exact relay, Ford or continuous you have.

The MAIN thing between them, and the reason you don't want to use a continuous to switch a starter, is this:

The contacts are rated at far less current. Part of the reason for this is the coil itself. Relay contact ratings in part depend on the amount of force closing them. Starter solenoids generate a LOT more contact closing force than do continuous, and the reason is that they have heavy coils that generate a lot of "pull." This of course is the very reason a Ford solenoid cannot be used continuously

The second thing is relay wiring. "The number of terminals" does not tell the story. Typical 12V Ford pass car / truck solenoids have what is commonly called a "grounded base," meaning that the S terminal and ground actuate the relay coil. The second small terminal, "I" was used for ballast resistor bypass for starting. The older GM starter solenoids are the same way.

But not all solenoids are wired that way. Some have two small terminals, and they are the coil terminals, sometimes called "insulated base." Most continuous solenoids either have 4 terminals, "insulated base," or three.....on small and two large, and they are "grounded base."

You cannot hook a Mopar neutral switch to a Ford solenoid. You CAN however use a "Ford like" solenoid that was used on AMC/ Jeep for a few years. These look just exactly like a Ford solenoid except they have an extra bullet "push on" terminal for the coil. So they are "insulated base" and also have the "I" bypass terminal. 5 total.