What about this:
All 13 celestial bodies have cores of the same material and "charge" (i.e. magnetic, atomic force, magical, aether, investiture, etc.) that repels similar substances (think electrons). Now add in gravity and the planet and moons are all attracted to each other as well, but moreso to the much larger planet. Once they reach a distance where the gravitational attraction force equals the magical repelling force, they should all settle into the aforementioned geometric shape. Maybe like how atoms and molecules can form a crystal given the right conditions. Add in some spin (or not, maybe the star revolves around the planet/moon structure) and the whole thing could plausibly keep its crystalline formation, more or less. To establish a geosynchronous "orbit" all you need is enough time and the planet should eventually converge in a tidally locked state with its moons.
As for the rock and spores, they aren't made of the same substance as the planetary cores and therefore the spores from the 12 "moons" are ultimately attracted to the planet. The moons are close enough to the planet that the gravitational forces attract the nearest spores, while the strong repelling force of the cores keeps the moons just off the surface.
Plausible? Barely. But who knows what's possible in a fantasy genre?
