Physics: Auto-stopping a spaceship with reverse thrusters

I'm playing with a concept for a spaceship game with physics. I have three rigidbody objects attached with fixed joints: a hull, a main engine, and a reverse thruster. There is no drag or angular drag. There is no gravity. The main engine and reverse thruster both have a "Thrust" script attached which uses AddForce to propel the ship forward or backward.

My goal is to create an "auto-stop" function for the ship. Basically, whatever the ship's (hull's) velocity is, I want a script to manipulate the engines' thrusts so the ship reaches a standstill.

As a test, I've been using the Z-axis only. The following code runs from an Update()...

     void Stop ()
     {
         Vector3 velocity = ship.GetComponent<Rigidbody>().velocity;
         Vector3 heading = ship.gameObject.transform.forward;
 
         float vx = velocity.x;
         float vy = velocity.y;
         float vz = velocity.z;
         float hx = heading.x;
         float hy = heading.y;
         float hz = heading.z;
 
 
 
         if (velocity != Vector3.zero)
         {
             if (vz == 0)
             {
                 Debug.Log ("The ship is not moving on Z");
             }
             else if (hz > 0 && vz > 1)
             {
                 mainEngine.GetComponent<Thrust>().output = 0;
                 reverseThruster.GetComponent<Thrust>().output = reverseThruster.GetComponent<Thrust>().maxThrust;
             }
             else if (hz > 0 && vz > 0)
             {
                 mainEngine.GetComponent<Thrust>().output = 0;
                 reverseThruster.GetComponent<Thrust>().output = 1;
             }
             else if (hz > 0 && vz < -1)
             {
                 reverseThruster.GetComponent<Thrust>().output = 0;
                 mainEngine.GetComponent<Thrust>().output = mainEngine.GetComponent<Thrust>().maxThrust;
             }
             else if (hz > 0 && vz < 0)
             {
                 reverseThruster.GetComponent<Thrust>().output = 0;
                 mainEngine.GetComponent<Thrust>().output = 1;
             }
         }
         else
         {
             Debug.Log ("The ship is stopped");
 
             mainEngine.GetComponent<Thrust>().output = 0;
             reverseThruster.GetComponent<Thrust>().output = 0;
         }
     }

It seems to work decently, though the ship never actually come to a complete stop. It still moves at a thousandth of a unit every second or two.

Should I move the code to work from a FixedUpdate() instead? Do I need to kill the engines and add in a small delay between checks, and if so, how? Or would I be better off just zeroing out the velocity directly through the script when it gets so low?

Thank you so much!