Confusion with Aron Granberg's A* Pathfinding

Hello people :)

I'm currently working on a turn-based project which requires pathfinding based on a hexagon grid, and have been looking into Aron Granberg's A* Pathfinding packages (which are extremely powerful from what I've seen so far).

But I've come up against a snag... I can't work out exactly how to make the unit (or game object, that is) move exactly along the path, consisting of a series of waypoints or 'nodes,' each in the centre of each hexagon which make up the grid.

What happens at the moment is that the unit travels in a straight line toward a waypoint, but it has a radius around it which searches for the waypoint to confirm the 'waypoint reached.' When this radius (say a radius of 1) touches the waypoint, the unit instantly starts moving toward the next waypoint, effectively cutting the corner of the turn. Scale-wise, think of the unit itself being say 0.2 radius, and the detection radius being about 1. This may seem ok in normal navigation, but it doesn't suit the hex-grid-based pathfinding I'm trying to accomplish.

Here's the code I have came up with so far...

 using UnityEngine;
 using System.Collections;
 using Pathfinding;
 
 public class AstarAI : MonoBehaviour {
     public Vector3 targetPosition;
     public GameObject targetNode;
     
     private Seeker seeker;
     private CharacterController controller;
     
     //the calculated path
     public Path path;
     
     //the AI's speed per second
     public float speed = 100;
     
     //the max distance from the AI to a waypoint for it to continue to the next waypoint
     public float nextWaypointDistance = 1;
     
     //the waypoint we are currently moving towards
     private int currentWaypoint = 0;
     
     public GameObject clickedObject;
     
     public Ray ray;
     public RaycastHit hit;
     
     public void Start () {
         controller = GetComponent<CharacterController>();
     }
     
     public void MyCompleteFunction (Path p) {
         Debug.Log ("Yay we got a path back! Is there an error?" + p.error);
         if (!p.error) {
             path = p;
             //reset the waypoint counter
             currentWaypoint = 0;
         }
     }
     
     public void Update () {
         //Find the closest node to this GameObject's position
         Node node = AstarPath.active.GetNearest (transform.position);
         ray = Camera.main.ScreenPointToRay(Input.mousePosition);
         if (Physics.Raycast(ray, out hit, 100)) {
             targetPosition = AstarPath.active.GetNearest (hit.point);
             Debug.DrawLine(ray.origin, hit.point);
             if (node.walkable) {
                 Debug.Log ("this is walkable" + node.position);
                 MoveOnThePath();
             }
         }
 
         if (path == null) {
             //we have no path to move toward yet
             return;
         }
         
         if (currentWaypoint >= path.vectorPath.Length) {
             Debug.Log ("End of path reached");
             return;
         }
         
         //direction to the next waypoint
         Vector3 dir = (path.vectorPath[currentWaypoint] - transform.position).normalized;
         dir *= speed * Time.deltaTime;
         controller.SimpleMove (dir);
         
         if (Vector3.Distance (transform.position, path.vectorPath[currentWaypoint]) < nextWaypointDistance) {
                 currentWaypoint++;
                 return;
             }
     }
     
     public void MoveOnThePath () {
         Seeker seeker = GetComponent<Seeker>();
         controller = GetComponent<CharacterController>();
         seeker.StartPath (transform.position, targetPosition, MyCompleteFunction);
     }
 }

Any help would be greatly appreciated!

Thanks, Aaron :)