I'll be honest here; I don't know much about the physics of planets and planetary systems, etc. However, I've been looking into ellipsoidal moons, and most of what I've found is about Nix, one of Pluto's moons. The problem with this is that Pluto is very different from Earth, and Charon changes Nix's orbit drastically.
So, without another moon half the size of the planet, how would an ellipsoidal moon orbit and spin? What would phases look like? And would a different moon shape have any effect on larger aspects of everyday life?