I don't know about "putting a second one down, and then picking up the first one," if you could do that then you could potentially have 2 cores on one ship....
What would that mean?
Instead I think (for now at least) there should just be a mechanic where perhaps in advanced build mode there's a button that says "move core" and if you click it then it will ask you where you want the core to be moved to. Then you click the new location and presto you now have 2-5 times the ship you had less than a second ago.
Perhaps this could cost some money to do? In an effort to prevent a "The Battle of Jumping-Core" scenario. Or perhaps a slight time delay like 10 seconds (I think the time one would work better).
Basically though, it would function largely the same as the current system by which you put down a new symmetry-mode plane, except I'm thinkin' it would be nice to have an "Are you sure?" prompt, so it's not done on accident.
However, even if this does cause some "The Battle of Jumping-Core" scenarios, I still think it would be worth it. It is SOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO annoying when you build a pretty ship that you can't use because you changed your plans as you were building it, and ended up with your core in/near the front.
Hoping this gets implemented,
-Prep :D