Well I completely uninstalled and reinstalled Starmade. That didn't work. I completely uninstalled and reinstalled Java. That didn't work. I ran all my CCleaner and Advanced System Care programs. That didn't work. I noticed that Nvidia released a new driver while I was away, and I uninstalled that and performed a clean install of a previous driver. Now Starmade magically works again, so if you encounter these issues in the future with other users, perhaps they have the latest Nvidia GeForce drivers and going back to a previous driver could solve it for them.

Update for you. I've since connected the entire assembly to the actual ship it goes on, so today I've been messing around getting the logic and alignment and whatnot in order to ensure that the mechanical functionality is working as intended. (There are actually two of these assemblies, one on top and one on bottom of the ship, which is why they needed to extend, there wasn't enough space for them to meet in the middle otherwise).

The very bottom platform is pretending to be the ship the rest of it attaches to. If you are going to test this on an actual ship then you won't need that part.

Here is the turret in question. It is a capital turret for a Klingon Ship, which can detatch and be a ship of its own. When you spawn this blueprint, enter into the core of the lowest platform. Go to Entity Structure, Rail System Collective, make sure you Deactivate AI Turrets and then Reset AI Turrets. You must do this before extending or retracting the assembly, though none of this is necessary to check the Missile issue. But you should know about it so that you don't run into other issues while playing with this.

I observed it in Build Mode. I moved to the loaction where the missile tubes are placed. There is an empty compartment around them. I go into flight mode, fire the missiles, then switch to Build Mode and see the missiles travelling to the right inside the compartment and colliding with the interior of the turret. If I go outside of the ship in Build Mode, I never see the missiles leave the ship. If I stay in Flight Mode while firing, I hear the explosions happening right next to me. If I lock on to a target, the missiles still never leave the turret. It is not a visual bug. The missiles fire to the right when the computer is oriented to the left. I can provide a .sment file if you'd like.