Have I got this right?
Engine starts on Easy Start but won't start / run normally so it is not injecting fuel.
This means that either you don't have a high pressure fuel supply or the ECM is not triggering the injectors
If the rail pressure sensor or its wiring was damaged then the ECM would substitute a default value and the engine should start.
Engine stopped when running so not the cam sensor and you have changed crank sensor so the ECM should know where the crankshaft is.
You have eliminated the HP pump so not that and you changed the fuel pressure regulator with the pump from a known working engine - should be OK.
Can you put a fuel pressure gauge on the high pressure fuel line to check that the HP pump is running?
If that is all OK then we have the low pressure fuel system - if the ECM does not think that the low pressure fuel is coming through then it will shut down the HP pump.
LP pump is priming so not the pump relay or the inertia switch but is there pressure at the inlet to the HP pump?
Could the LP fuel sensor be faulty / disconnected?
When you changed the fuel filter did you run the LP pump? - I remember a recent thread on LZ where somebody found a foreign body in the fuel line that was restricting flow.
Can't think of anything else for now but without some fuel pressure readings this is going to be largely guesswork