How to design a smooth up/down UI scroll inside Update() for a joystick input?

I am developing a VR application in Unity and I am struggling to develop a smooth UI scroll using my VR controller's joystick. So far what I have looks like this...

Code (CSharp):

1. private void Update()
2. {
3.     float joyStickDirection = globals.menuInteraction_Scroll.GetAxis(SteamVR_Input_Sources.Any).y; // this is either 1 for up or -1 for down
4.     if (joyStickDirection != 0)
5.     {
6.         float multiplier = joyStickDirection * 5f;
7.         scrollRect.verticalNormalizedPosition = scrollRect.verticalNormalizedPosition + (multiplier * Time.deltaTime);
8.     }
9. }

...this works, but has two problems. Firstly, it scrolls at different speeds depending how big the scrolling container is. Secondly, the scrolling is not very smooth, as it is clearly just skipping varying gaps between 0 and 1.

I think I know what's wrong but I don't have enough experience working inside Update() to figure out the correct approach. Can anyone advise?

 

I can also switch joyStickDirection to capture how far the joystick is pushed so it's any point from -1 to 1 instead of just -1 or 1.

 

Settled for this strategy:

Code (CSharp):

1. public class ScrollExample : MonoBehaviour
2. {
3.     public float speed = 5f;
4.  
5.     public Transform ScrollContent;
6.    
7.     void Update()
8.     {
9.         // this is either 1 for up or -1 for down
10.         var joyStickDirection = globals.menuInteraction_Scroll.GetAxis(SteamVR_Input_Sources.Any).y;
11.         if (joyStickDirection != 0)
12.         {
13.             var multiplier = joyStickDirection * speed;
14.            
15.             // You want to invert the direction since scrolling down actually means
16.             // moving the content up
17.             ScrollContent.position -= Vector3.up * multiplier * Time.deltaTime;
18.         }
19.     }
20. }