My logic on the design: Abydos's Point of Origin Glyph was a Pyramid with three moons that were visible even during the day, clearly the most prominent sight the local's would think of for their Home Symbol. Earth's two gates have similar logic- the Antarctic Backup Gate was simply of a circle above the flat ground- likely the most common view seen from Antarctica- and the Giza gate was of the Pyramid with the Sun ontop, also very familiar to the humans of Egypt at the time.
Thus, Alternia's Home Symbol HAS to have a similar logic to it- even if it's one being retro-actively applied if the gate has been moved from planet to planet. So, Alternia's most commonly seen Celestial Bodies is it's three moons: The Two PINK MOONS being closest to the planet, and the smaller, GREEN MOON further away. The "PYRAMID" then, can either be an ancient structure, OR, as repurposed by the Condesce, a representation of the front bow of her BATTLE SHIP.