Although this is explicitly at odds with the author's intentions, I don't think there should be an overlap of any kind between "moon" and "planet." So I'd modify his definition of "A planet is a sub-stellar mass body that has never undergone nuclear fusion and that has sufficient self-gravitation to assume a spheroidal shape adequately described by a triaxial ellipsoid regardless of its orbital parameters" to add: "excluding any object that orbits a point located within a planet." Thus our Moon would remain a moon but Pluto-Charon could be a double planet because the point they revolve around is not within either body.