Keep camera from rotating around relative z-axis - unity3d

Question

I'm trying to create camera movement that mimics the behavior of the unity scene editor where you can perform a spherical rotation around the scene with 2d mouse movement. So far the camera is rotating correctly given x or y movement, but dragging diagonally causes the camera to rotate around its relative z-axis until it gets locked. I cannot force the camera to look at the origin relative to world up because then it cannot rotate upside-down
Here is the script that I've attached to the camera
using UnityEngine;
public class MainCamera : MonoBehaviour
{
Vector2 startingPosition;
Vector2 mousePosition;
Vector3 orthogonalCameraVector;
float degreesPerUnitWidth = 180f / Screen.width;
float degreesPerUnitHeight = 180f / Screen.height;
float cameraRadius = 10;
void Start()
{
transform.position = new Vector3(0, 0, -cameraRadius);
transform.LookAt(Vector3.zero);
orthogonalCameraVector = -Vector3.left;
}
void LateUpdate()
{
if (Input.GetMouseButtonDown(0))
{
mousePosition = Input.mousePosition;
}
if (Input.GetMouseButton(0))
{
var input = new Vector2(Input.mousePosition.x ,Input.mousePosition.y);
startingPosition = mousePosition;
var mouseDelta = startingPosition - input;
var xzDegrees = -mouseDelta.y * degreesPerUnitHeight;
var xzRotation = Quaternion.AngleAxis(xzDegrees, orthogonalCameraVector); // rotate about the relative x-z plane
var yRotation = Quaternion.AngleAxis(-mouseDelta.x * degreesPerUnitWidth, Vector3.up); // rotate about the world y-axis
var rotation = xzRotation * yRotation;
orthogonalCameraVector = rotation * orthogonalCameraVector;
transform.position = rotation * transform.position;
transform.rotation = rotation * transform.rotation;
mousePosition = Input.mousePosition;
}
}
}

Answer 1

I realized the orthogonalCamerVector only needed to be rotated about the y-axis because I wanted to keep it parallel with the xz-plane. I then applied this rotation to the orthogonalCamerVector before rotating the transform so it would always be rotating about a fixed plane so it looks something like this:
var xzDegrees = -mouseDelta.y * degreesPerUnitHeight;
var yRotation = Quaternion.AngleAxis(-mouseDelta.x * degreesPerUnitWidth, Vector3.up); // rotate about the world y-axis
orthogonalCameraVector = yRotation * orthogonalCameraVector;
var xzRotation = Quaternion.AngleAxis(xzDegrees, orthogonalCameraVector); // rotate about the relative x-z plane
var rotation = xzRotation * yRotation;
transform.position = rotation * transform.position;
transform.rotation = rotation * transform.rotation;