Smooth scroll snap?

I currently have my menu working almost perfectly except I want to enable smooth scroll snapping to each element in the menu. I currently have a script that lerps the scrollbar value to the nearest snap point when the user isn't scrolling but although this is quite clean, it makes the user have to drag a distance bigger than is comfortable, and I just want a swipe to take them to the next one (it's not necessary for a big swipe to take them multiple items down, but that would be nice)

Below is the script I'm using right now, and a demo I found that is exactly what I want (but it's CSS so not really transferable):

What I want: http://codepen.io/sdras/pen/43c9d13b23bc34a85bb3a5e2ea985958

This script is attached to both the scrollbar to control the value, and the ScrollRect to get access to whether it is scrolling or not, and a static value to sync the values between instances:

 using System;
 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.EventSystems;
 using UnityEngine.UI;
 
 public class UI_SmoothScrollSnap : MonoBehaviour, IBeginDragHandler, IEndDragHandler {
 
     public float SnapSpeed = 10;
     public float ScrollVelocity;

     [ShowInInspector] //I added this outside of my IDE so not sure if it's the right attribute
     private bool isDragging;
     public int Snaps;
     public static bool Dragging;
 
     private Scrollbar scroll;
     private ScrollRect sRect;
 
     // Use this for initialization
     void Start () {
 
         scroll = FindObjectOfType<Scrollbar> ();
 
         sRect = FindObjectOfType<ScrollRect> ();
         
     }
     
     // Update is called once per frame
     void Update () {
 
         isDragging = Dragging;
 
         if (!scroll)
             return;
 
         //ScrollVelocity = sRect.inertia.y;
 
         if (!Dragging)
             scroll.value = Mathf.Lerp (scroll.value, Mathf.Round (scroll.value * (Snaps - 1)) / (Snaps - 1), SnapSpeed * Time.deltaTime);
         
     }
 
     public void OnBeginDrag (PointerEventData eventData) {
         Dragging = true;
     }
 
     public void OnEndDrag (PointerEventData eventData) {
         Dragging = false;
     }
 
 }