I understand that your fuel pressure gauge is installed downstream of the fuel shut off solenoid and just before the high pressure injection pump ... is this correct?
You said your "fuel pressure was staying above 6-1/2 psig through the whole test". Was the pressure fluctuating any during the test? How about just prior to shutting down ... did the pressure change then.
If the fuel pressure was rock solid, than any component upstream of the pressure gauge should be working fine ... eliminating any blockage in the fuel delivery system and also eliminating the fuel shut off solenoid I would
deduce. That being said, I think it would still be good to check out the fuel shut off solenoid ... despite what your pressure gauge says.
More brain storming - we know you show pressure coming from your new electric pump. Just for shxts and giggles, I would disconnect the fuel supply line going into the injection pump and measure the rate of fuel delivery. Use a cup of a know volume and measure the time to fill or partially fill it to determine the fuel pump rate. It would be worth doing when the engine is cold and again after it has failed after warming up. If you have a good fuel delivery rate both cold and warm, then that eliminates a lot of guessing.
And some more brain storming - How about sensors ... like I mentioned earlier, perhaps a faulty sensor (oil pressure, air sensor, others?) that is killing the engine when it warms up. Does anyone have a wiring diagram for this machine to see how the sensors work? I assume the sensor would kill the engine using the fuel shut off solenoid ... but that is just a guess, not based on any personal experience.