BoxCollider2D is mysteriously offset by a slight but obvious amount

Could you post some of your code on how you are getting the box collider using raycast? Is your object a child of another object? You may need to offset the position you got by your objects transform.

       // Update is called once per frame
     void Update () {
 
         // Perform a raycast from the UICamera to discover what the
         // mouse is hovering over
         Ray ray = cameraUI.ScreenPointToRay(Input.mousePosition);
         RaycastHit2D hit = Physics2D.Raycast(ray.origin, ray.direction);
 
         if(hit != null && hit.collider != null)
         {
             // this converts cube to sphere
             if(hit.collider.name == "SpeedControlLever")
             {
                 Debug.Log("hit lever");
             }    
             else
             {
                 Debug.Log("didn't hit lever");
             }
         }
     }

Offsetting the BoxCollider2D does fix the symptoms of the problem, but, does not address the mysterious underlying cause.

Allow me to suggest a few "sanity-checks": Use Debug.Log to display the mouse position, AND the bounds of the collider when you hit (https://docs.unity3d.com/ScriptReference/Collider2D-bounds.html).

You can also use Gizmos.DrawWireCube to display the bounds in the scene view, to confirm it matches up with what the editor shows.
Better yet, create a Cube primitive, assign it's position to the bounds center, and scale to the bounds size. This object will be visible in the camera view, and should show the area of the collider.

@Hexagonius how would local/global stuff affect that code?