Thinking about slightly revamping phases:

I generally think of Fate as being the TV Show RPG, and say that the first session usually lands somewhere around episode 6.  So maybe it's worth re-framing the three phases as being individual episodes that occur prior to episode 6?  So instead of some nebulous backstory, it's focused more concretely on the things that this group has done together after they've met, or at least in the process of meeting.  It would likely also do away with some of the time-ordering issues that I see come up in the phases a lot.

This is probably something that's how most people already think of it, but there it is :)