Make GameObject “attach” properly?

This script makes a cube "stick" to whatever it collided with. The problem is that when it's going at relatively high or medium speeds (or when the device itself is slow), the cube tends to "get a bit inside" what it collided with and then stick to it. What changes do I have to make to fix this?

In order for this script to work, one GameObject must have bool _sticksToObjects = true; and the other bool _sticksToObjects = false;

I have tried turning the Rigidbody's Collision Detection mode to either Continuous or Continuous Dynamic

I think my script depends on frame rate. That may be where the problem lies.

Normal "Attach":

see here

Abnormal "Attach":

see here

 Rigidbody _rigidBody;
 Transform _meshTransform;
 bool _sticksToObjects = true;
 
 public Transform _stuckTo = null;
 protected Vector3 _offset = Vector3.zero;

 void Awake()
 {
     GameObject CubeMesh = GameObject.FindWithTag ("CubeMesh");
     GameObject Cube = GameObject.FindWithTag ("Cube");

     _rigidBody = Cube.GetComponent<Rigidbody> ();
     _meshTransform = CubeMesh.GetComponent<Transform> ();
 }

 void LateUpdate() 
 {
     if (_stuckTo != null)
     {
         transform.position = _stuckTo.position - _offset;
     }
 }
 
 void OnCollisionEnter(Collision collision)
 {
         if (!_sticksToObjects) {
             return;
         }
             
         _rigidBody.isKinematic = true;
     
         // Get the approximate collision point and normal, as there
         // may be multipled collision points
         Vector3 contactPoint = Vector3.zero;
         Vector3 contactNormal = Vector3.zero;
         for (int i = 0; i < collision.contacts.Length; i++) {
             contactPoint += collision.contacts [i].point;
             contactNormal += collision.contacts [i].normal;
         }
     
         // Get the final, approximate, point and normal of collision
         contactPoint /= collision.contacts.Length;
         contactNormal /= collision.contacts.Length;
     
         // Move object to the collision point
         // This acts as setting the pivot point of the cube mesh to the collision point
         transform.position = contactPoint;
     
         // Adjust the local position of the cube so it is flush with the pivot point
         Vector3 meshLocalPosition = Vector3.zero;
     
         // Move the child so the side is at the collision point.
         // A x local position of 0 means the child is centered on the parent,
         // a value of 0.5 means it's to the right, and a value of -0.5 means it to the left
         meshLocalPosition.x = (0.5f * contactNormal.x);
         _meshTransform.localPosition = meshLocalPosition;
     
         if (_stuckTo == null || _stuckTo != collision.gameObject.transform) {
             _offset = collision.gameObject.transform.position - transform.position;
         }
     
         _stuckTo = collision.gameObject.transform;
     }

Here are some screenshots of the Unity editor:

Screenshot 1: i.stack.imgur.com/ivA6F.png

Screenshot 2: i.stack.imgur.com/9XGpv.png

Screenshot 3: i.stack.imgur.com/XP8G2.png