Sorry mate i didnt see the blown fuse thing to start with. Yes replacing that fuse is 99.9% the answer to your cold start problem, thats the fuse for the fuel ECU main power supply. I think you still have the factory Fuel Injection Module Relay looking at it, but the wrong fuel pump relay. The fuel pump relay isn't a biggy but you don't have the rev limiter function.

And the only other thing i was going to say, and no offence, but that wiring is didn't you say it was already like that when you got it?