After replacing the fuel pump did you put Protune 2 on the ECU and clear the adaptive maps? The original pump may well have been operating at less than a regulated 58 psi for some time and the adaptive maps will....adapt. With the new pump you should be operating at a steady regulated 58 psi (check this at the Schrader test point on the RH injector body) but the adaptive maps will be still working for a lower delivery pressure maybe? It's a good idea to "zero" the ECU after the fuel pump change anyway.
As the problem has only started since the fuel pump change, it is logical to think it is related to that but it will still be sensible to check all the other things like plugs and leads, you never can tell with a M3W. I assume you don't touch the throttle pedal when cranking? It's a bad idea as the ECU zeros the throttle position every time the ignition is turned on and gets a false figure if you touch it.
