First thing I would check is to see if your fuel pump check valve leaks a little and is allowing the fuel pressure to drop off overnight. If you don't want to go through the hassle of installing a fuel pressure gauge, you can get an idea if that's what's going on simply by pressurizing the fuel system before you try to start the car.
On those mornings when the problem "would normally occur", pull the starter solenoid wire off and turn the key to START to get the fuel pump to run without engaging the starter. Then after a couple seconds of that, put the wire back on and then try to start the engine normally. If it starts instantly, then that's probably what's happening. If it still takes just as long to start even after making sure there is fuel pressure, then maybe there's an issue somewhere else.
I've removed my cold start injector, so mine takes a couple cranks to start because of that. I'm OK with the delay as a trade off for fewer leak locations and simplicity.