Jerky motion and inconsistent collision detection with planes with rigid bodies

I have a prefab made up of a plane + rigid body + collider, a "selection tracking" script attached to the main camera and global gravity set to 0 in all directions. I'm trying to be able to instantiate prefabs on mouse / touch up and drag existing ones around.

Here's my prefab:

And this is my "selection tracking" code:

 using UnityEngine;
 
 public class SelectionTracker : MonoBehaviour {
     public GameObject node;
     
     public class UniversalTouch {
         public Vector2 position;
         public TouchPhase phase;
         
         public UniversalTouch(Touch touch) {
             this.position = touch.position;
             this.phase = touch.phase;
         }
         
         public UniversalTouch(Vector2 position, TouchPhase phase) {
             this.position = position;
             this.phase = phase;
         }
     }
     
     UniversalTouch currentTouch;
     GameObject currentlySelectedObject = null;
     
     //    MonoBehaviour:--------------------------------------------------------------------------------------------------
     
     void Start() {
         currentTouch = null as UniversalTouch;
     }
     
     void FixedUpdate() {
         updateTouch();
         if (currentTouch != null) {
             switch (currentTouch.phase) {
                 case TouchPhase.Began: {
                     RaycastHit hit;
                     if (Physics.Raycast(camera.ScreenPointToRay(currentTouch.position), out hit)) {
                         GameObject node = hit.transform.gameObject;
                         if (node != null) {
                             currentlySelectedObject = node;
                             currentlySelectedObject.rigidbody.isKinematic = true;
                         }
                     }
                     else {
                         currentlySelectedObject = null as GameObject;
                     }
 
                     break;    
                 }
                 
                 case TouchPhase.Moved: {
                         if (currentlySelectedObject != null) {
                             currentlySelectedObject.transform.position = camera.ScreenToWorldPoint(new Vector3(currentTouch.position.x, currentTouch.position.y, -camera.transform.position.z));
                         }
                     
                     break;    
                 }
                 
                 case TouchPhase.Stationary: {
                     break;    
                 }
                 
                 case TouchPhase.Ended: {
                 if (currentlySelectedObject == null) {
                     Vector3 newNodeLocation = camera.ScreenToWorldPoint(new Vector3(currentTouch.position.x, currentTouch.position.y, -camera.transform.position.z));
                         GameObject newNode = (GameObject)Instantiate(node);
                         newNode.transform.position = newNodeLocation;
                 }
                 else {
                     currentlySelectedObject.rigidbody.isKinematic = false;
                 }
                     break;    
                 }
             }
         }        
     }
     
     void updateTouch() {        
         if (Input.touchCount == 1) {
              currentTouch = new UniversalTouch(Input.touches[0]);
         }
         
         Vector2 newScreenPosition = new Vector2(Input.mousePosition.x, Input.mousePosition.y);
         if (Input.GetMouseButton(0)) {            
             if (currentTouch == null) {
                 currentTouch = new UniversalTouch(newScreenPosition, TouchPhase.Began);
             }
             else if (currentTouch.phase == TouchPhase.Began || currentTouch.phase == TouchPhase.Stationary || currentTouch.phase == TouchPhase.Moved) {
                 if (currentTouch.position == newScreenPosition) {
                     currentTouch.phase = TouchPhase.Stationary;
                 }
                 else {
                     currentTouch.phase = TouchPhase.Moved;
                     currentTouch.position = newScreenPosition;
                 }
             }
         }
         else if (currentTouch != null) {
             if (currentTouch.phase == TouchPhase.Stationary || currentTouch.phase == TouchPhase.Moved) {
                 currentTouch.phase = TouchPhase.Ended;
                 currentTouch.position = newScreenPosition;
             }
             else {
                 currentTouch = null as UniversalTouch;
             }
         }    
     }
     
 }

However, I have two problems with this approach:

1. When I select an existing prefab and drag it around, it doesn't feel smooth but somewhat jerky.

2. If I drag whichever prefab I select around fast enough, it does intersect other prefabs. That is, for the one I'm dragging to repel off any other prefabs, I have to drag at a somewhat intermediate speed.

I tried solving these issues by:

• Replacing Update with FixedUpdate

• playing around with the different interpolation and collision detection modes in the rigid body

• switching whichever prefab I am dragging to kinematic.

But I still have the same problems. Any thoughts on what am I doing wrong?