I believe there is another game that does this, where you build ships on different levels, but when the ships are in action, you only see the top level, but the other levels items still function as normal. The game should be able to easily remember what is on each level of a ship, and being able to switch between each level of the ship is a matter of adding a selector to create new level of the same size as the previous level, just completely empty.
I would go so far as to say that some items should also be more than one story tall. The factories and the reactors would be 2 stories tall, so they would stick up into the new level. The larger weapons could also be two stories tall, while the smaller lasers and cannons could only take up the level they are placed in.
I do believe this is very doable with what you have in the game currently, and while it would take some more work on your part, I believe the addition to multiple leveled ships would greatly increase the immersion this game gives the player. Please do put some thought into adding it, and if you want to see how another game managed it, let know me.