What I'm saying is that without firing rockets, there's nothing you can do to change the trajectory of your centre of mass. When you "extend" the cable towards earth, presumably you are pushing on it in some way, and there will be an equal and opposite reaction. You don't have to "carefully move the ship outwards" - the ship (which is inherently "massy", as it has the rest of the cable as cargo) will move outwards by itself, exactly the right amount for the centre of gravity of the ship-cable system to remain in geostationary.

So I still don't see what two cables gets you apart from keeping the ship itself exactly at geostationary, which strikes me as unimportant.