Somebody with more experience might pinpoint right away the problem based on your fuel delivery problem only when cold starting. A lot mention the fuel regulator. I wonder if an experienced mechanic would need to go through a pressure test to pin point the problem given the syptom. I would measure the pressure during cranking. Assuming it was too low I'd test again with the return hose pinched temporarily. If it then starts the regulator would be my bet, if not I'd wonder about other possibilities.