Controlling speed of diagonal navmesh movement?

Hi all. I've been working on a navmesh-based character controller based on this great video from Ciro Continisio. Here's how I adapted his code to work with the old Input Manager:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.AI;
 
 public class PlayerMovement : MonoBehaviour{
   public float speed = 10f;
 
   private Vector3 inputValue = Vector3.zero;
   private float inputSqrMagnitude;
 
   void Update(){
     Step();
   }
 
   private void Step(){
     inputValue = new Vector3(Input.GetAxis("Horizontal"), 0f, Input.GetAxis("Vertical"));
     inputSqrMagnitude = inputValue.sqrMagnitude;
     if(inputSqrMagnitude >= .01f){
       Vector3 newPosition = transform.localPosition + inputValue * Time.deltaTime * speed;
       NavMeshHit hit;
       bool isValid = NavMesh.SamplePosition(newPosition, out hit, 1.0f, NavMesh.AllAreas);
       if(isValid){
         if((transform.localPosition - hit.position).magnitude >= .02f){
           transform.localPosition = hit.position;
         }else{
           // movement stopped this frame
         }
       }
     }else{
       // no input from player
     }
   }
 }

This has been helping me prototype levels very quickly, but I've noticed that diagonal movement is much faster than single-axis movement. Typically this can be controlled by normalizing or clamping the magnitude of the target vector, but I'm not sure how to do that here. I've tried the following:

• transform.localPosition = Vector3.ClampMagnitude(hit.position, speed); causes character to teleport diagonally and get stuck in the terrain after any WASD input

• transform.localPosition = hit.position.normalized; does the same

• newPosition = Vector3.ClampMagnitude(newPosition, speed); also causes the character to teleport, but they can still move within a small circular area in the level

• newPosition = newPosition.normalized;, which leaves the character unable to move at all

Any ideas?