The reason to replace the thermostat is to eliminate any possibility the thermostat has anything to do with you problem. I don't think that is the case, highly unlikely, but the electronics do read engine heat and do adjust fuel/air mix.

Pinching the return line with the engine running increases the pressure at the engine and could account for the engine running normally. The same is true when you were doing the test at the fuel rail. It would start but if you waited until the pressure built up some it would fire and then stall. When you tried to start it right away there wasn't enough pressure to fire up the engine.

This is important---Is it correct that the original symptoms and the symptoms after the 500 good miles were exactly the same? If that is the case and the replacement fuel pump was the fix the first time, it is very logical to expect the same symptoms indicate the same solution.

Since you have replaced the pump twice, it is logical to check if the voltage to the pump is constant.

I would repeat the last test with the engine not running. If the test of pinching off the return line, with the engine not running, does not show a rapid increase in the pressure when the line is pinched, I would assume the pump is not working right.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas