Have a 2000 f350 7.3 super duty. The starter stayed engaged and I was unable to turn off the motor, although turning the ignition back to off, the starter stayed on. Ultimately the starter burned out and was shot. I replaced the starter and the ignition tumbler in the steering wheel. Work for a day then the starter again stayed engaged and did the same thing. I disconnected the batteries to shut the truck off, yes I know its bad but didn't want to burn up another starter. What is going on?
The starter circuit is typically quite simple. The high current wire goes from the battery to the starter motor. The ignition sends a signal to a relay so it closes and allows current to flow to the starter solenoid. The solenoid engages the starter motor teeth with the flywheel teeth, and simultaneously connects the high current power to the starter motor. On some Fords, like yours (from what I've read), the relay portion of the solenoid is separate from the starter. It is a small part on the passenger side of the car, and it gets the signal from the ignition instead of a smaller relay activating the solenoid on the starter.
Since you've already replaced your starter and the ignition switch, you have one likely problem left.
The starter relay is dealing with significant current, so that's what you should test. You should not see any continuity between the battery terminal and the starter terminal (the two big terminals) with the battery disconnected, so if there is then that's your problem. On newer Ford trucks, there are two relays that look similar along the passenger side fender. You'll need the one further back from the front of the truck. It looks like this: