As said it has done this sort of thing since it was 2 years old. Not only does it go when started but it goes like stink (remapped). It will start fine again once started within say an hour or so, overnight not a chance in hell.
It is fuel, we know this 100%. No doubt about it.
I'd read the post above fully, the story explains it all really, a skim read will not furnish you with the full picture.
I did read it, you left out the part where it starts up if left less than an hour, you made it sound like it wouldn't start at all after turning off. And yes, fuel would be an issue, hence the crank position sensor which controls when the ECU fires the injectors. It's something to think about if it doesn't start when you put the system back together.