Another thing I'd not mentioned.
My car has a Global Telematics Thatcham immobilizer fitted.
It's a "key present" system, so you basically disarm it and start engine immediately.
I also wonder if this were not there the OEM systems would run the fuel pump for a second or two to pressurize the rail before cranking ?. I don't seem to be hearing others saying they have the same problem so maybe the OEM BMW / MMC system is sound after all ?.