I hope you'll get a reply from someone more knowledgable than I, but that sounds more like the solenoid than the starter motor. What seems strange to me is that the starter motor would run before being engaged by the solenoid. Could this be a wiring problem? I see from your other posts that this is an '87 -- is that the last year of the bad wires or the first of the good ones?

There is a check valve on the main fuel pump that's supposed to maintain pressure in the fuel line, nowhere near the tank. Is that what you're thinking about? I don't think that would cause your problems even if it were missing.

And with respect to the AMM -- did you try disconnecting it and see if that allows the car to start? I don't know anything about it, but I've seen that as the first test in diagnosing the AMM.