I think you have to research a certain level of Ship Construction or Base Construction to get the appropriate shipyard... so you can't get Base Yard III until you get Starbases, not sure what the levels for ship yards are...
OK, my turn for a question...
How come the "larger" base PD mounts don't actually take up more space? They have more hitpoints... the Massive Base PD actually make nice non-hit-first armor, with their 80 HP