How to properly make an object follow the edge of another object?

I want to have a cover system which works so that if the player is near a object big enough and presses the crouch key he hides behind that object basically meaning he is in a crouch animation and can move along it with A and D keys to side to side (Picture), I made this script but with this the speed variable for the movement while crouched doesn't seem to be taken into account, the thing causing it is the transform.position = coverPos; line and I can't find any other way to make the player "snap" to the edge of the other object so any help? The raycasting/cover "snapping" code:

 if (Physics.Raycast(coverBottom.position, coverBottom.TransformDirection(Vector3.forward), out hitB, 1.5f, layerMask))
         {
             coverPosition = hitB.point + hitB.normal * 0.3f;
             coverPosition.y = 0f;
             if (inCover)
             {
                 Vector3 lastNormal = Vector3.zero;
                 Vector3 coverPos = new Vector3(coverPosition.x, transform.position.y, coverPosition.z);
                 transform.position = coverPos;
                 transform.forward = -hitB.normal;
             }
         }

The player movement code: (There's lot more of course this is just that one part of it)

 public float walkSpeed = 2;
 public float runSpeed = 4;
 public float crouchSpeed = 0.5f;
 public float animationWalkSpeed = 1;
 public float animationRunSpeed = 3;
 public float animationCrouchSpeed = 0.5f;

 else if (!inputController.Run)
                     {
                         if (inputController.Cover || inCover)
                         {
                             crouch = true;
                             playerAnimator.SetFloat("speed", animationCurrentSpeed);
                             decreaser = runSpeed;
                             decreaser = Mathf.Clamp01(Time.time - secondsTillMaxSpeed);
                             currentSpeed = Mathf.Lerp(walkSpeed, crouchSpeed, decreaser);
                             animationCurrentSpeed = Mathf.Lerp(animationWalkSpeed, animationCrouchSpeed, decreaser);
 
                             float yStore = moveDirection.y;
                             if (inCover && h > 0)
                             {
                                 moveDirection = transform.right * currentSpeed * Time.deltaTime;
                             }
                             else if (inCover && h < 0)
                                 moveDirection = -transform.right * currentSpeed * Time.deltaTime;
                             else if (!inCover && h != 0)
                                 moveDirection = transform.forward * currentSpeed * Time.deltaTime;
 
                             moveDirection.y = yStore;
                             characterController.Move(moveDirection * Time.deltaTime);
                         }
                     }