How to lock an object's transform.forward?

I'm trying to lock an object a certain distance from a wall, so the player can move up/down and side to side, but can't move away from the wall.

Right now, my code looks like this:

 RaycastHit hit;
 LayerMask mask = LayerMask.NameToLayer("Wall");
 if (Physics.Raycast(this.transform.position, transform.forward, out hit)) {
     Vector3 normal = hit.normal;
     distance = hit.point + (-transform.forward * wallDistance);
     this.transform.position = new Vector3(this.transform.position.x, this.transform.position.y, distance.z);
 }

And in Update, the player will be kept distance wallDistance away from the wall.

Problem is, this will only work if the player is hitting a wall along the z axis. If the player were to instead be running along the x axis, and they hit a wall, they'd be unable to move side-to-side along the wall (z-axis), while able to move away from the wall (x-axis).

My question is, how do I lock the player in a certain value of transform.forward, while simultaneously allowing movement in transform.right and transform.up?