This is quite good
As I went along with my "franchise" in the early days I was more concerned about the political make up - This world I created is actually situated in another membrane universe, but for strange unknown reasons the inhabitants were formed to be like the creatures and entities from the imagination, folk law, nightmares and collective unconsciousness of humans on Earth.
Somehow a number of the higher order intelligent beings became aware of the existance of Earth and humanity, and using what they considered "magic",
(But as ever in this kind of thing never explained), they had constructed devices to travel between their universe and ours. In the earlier story lines I had it that some of the ancient gods humans worshiped were actually entities from the other world in human form. As time wore on and humanity grew up, the entities mostly returned to their world, although some stayed and the forces of law and order in the other world considered it a crime to further interfere in our world. A law, for storyline purposes was clearly honoured in the breach.
In the later storylines I did, I had a collusion of agencies from that world and secret Earth agencies to keep the existance of this alien world in another universe secret and to monitor those entities living among us
(Men in Black - Shades of)
This franchise has been kind of going since 2001, but I ressurected it last year. Only in some of the more recent story lines was I turning to the geography, my next story line I am half thinking of definitely requires more thought given to how this world would actually work.
In terms of the binary star system, I thought of something like Tatooine from the original Star Wars, so the suns are close together and the world orbits both.
In terms of the moons, in one of the more recent story lines I had a description where three of the moons were in the night sky, but it would be a lot later in the night before the forth one appeared.
eburacum45 idea is intriguing, with that set up, which would be the late moon one wonders, or perhaps over time each one would have turns of being late. One question, how would one get a retrograde moon, do any of our planets in the solar system have a moon that orbits backwards to others around the same planet?
As for formation, our moon is thought to be the result of a collision between two worlds where a larch chunk broke of and became the moon. Perhaps you could have this scenario, and then there was a further collision, either with the planet, or the moon.
So how did Larry Niven work out his Ring World?, I understand that he got quite a load of flack at a sci fi convention once by a rampaging mob of respectable physicists - or was that the inventor of the infinite improbability drive 