I am not sure how Honda assigned the order for that list of causes for 'Engine will not start'. Anecdotal evidence from NSX Prime forums would suggest that as the cars age the Main FI relay should be at the very top of the list as a probable cause. The list has it as the third item to check. It also lists the clutch interlock as the second last item to check for fail to start and again the infamous plastic clutch interlock actuating button (commonly known as the f*****g clutch interlock button by anybody who has had to replace it) is an anecdotally common failure point as is the ignition switch. Those causes are appropriately at the top of jwmelvin's troubleshooting flow chart. The original cause list was probably generated as check points for a 'newish' car where normal component aging was not a factor. We are now dealing with component aging which changes the probability of things that can stop the car.
As I recall from your posts, when your car does start it runs fine. That suggests that causes 4 (ignition system), 5 (CKP CYP sensor), 19 (contaminated fuel), 13 (clutch interlock), 1 (ECM) are likely not the cause. If it was 13 it would never start and if it was the others you should have driveability symptoms. That comment does not rule out the possibility that you have something like a bad / intermittent electrical connection which is causing the ignition system or ECM to be inoperative on occasion.
You ask about testing the fuel pump relay. In 'NSX speak' the fuel pump relay is the relay that by-passes the fuel pump resistor. The fuel pump is switched on by the PGM-FI (main relay) that you have replaced, not the fuel pump relay. Failure of the fuel pump (resistor by-pass) relay should not disable the car. It will result in low fuel pressure and bad operation under high engine load (pedal to the metal). Failure of the actual fuel pump resistor will prevent the car from starting. However, I would expect a failed resistor to stay failed rather than fail intermittently. Taking the fuel pump relay and the fuel pump resistor out of the equation for testing purposes is relatively easy. All you need to do is by-pass the resistor with a suitable shunt. If you search NSX Prime for fuel pump resistor by-pass I suspect you will find a couple of threads with pictures showing the location of the resistor and the connecting plug and how to by-pass the resistor. By-passing is relatively easy to do.
You noted that you have installed the remote electric fuel pressure gauge. If the gauge indicates that your fuel pressure is in spec when the engine fails to start, then you have taken failure of the fuel supply system out of the equation and it is time to start looking at the ignition system and the ECM, probably focusing on intermittent electrical problems. If the fuel pressure gauge indicates no or inadequate fuel pressure you will need to check for voltage to the pump. The test point is easy (just use the fuel pump by-pass resistor plug); however, the test is complicated by the fact that you need to test for voltage while the fuel pump is getting its 2-3 second prime pulse. In a failed start that is the only time that voltage is applied to the pump so you need somebody to turn the key and somebody in the engine bay with a voltmeter watching for voltage or temporarily connect a 12 volt test light to the test point and string it into the cockpit so that you can watch it when you turn the key.
The dealer's suggestion about using the spare key is interesting. However, two things. If the key is working correctly the immobilizer indicator light on the dash will come on for 2 seconds and then should go out. If the immobilizer light comes on and then starts blinking after 2 seconds that is an indication that the key code has not been read (key problem) or that there may be a problem with the immobilizer. I also seem to recall that the immobilizer ties into the starter cut relay system so if the chip in the key is not being read or the immobilizer is messed up the starter motor should not engage. If your starter motor is engaging then the immobilizer is likely OK. My service manual is locked up in my NSX which is locked up in secure storage so I can't confirm the bit about the immobilizer blocking the starter motor. You could check your service manual to confirm that. However, if the indicator light is giving you the correct indication and the starter motor is engaging I think your key and immobilizer system is probably OK.
