Make object lay flat on a sphere + look up?

Looking around I found a youtube video (at https://www.youtube.com/watch?v=gHeQ8Hr92P4) which explained how to make a object, such as a player character, walk around on a sphere while keeping its "head" facing upwards, even if it is on the side or bottom of the "planet".

His code works, but has a problem. The problem is, if I attach the "player" to my mouse, and move it around on the planet surface using my mouse, I notice that even though it DOES stay upright on the planet, it continually changes the direction it is "facing" as I move it around.

Here is the code (it works):

 Vector3 gravityUp = (player.position - planet.position).normalized;
 Vector3 playerUp = player.up;
 var horizontalRotation = Quaternion.FromToRotation (playerUp, gravityUp) * player.rotation;
 player.rotation = horizontalRotation;

Alright, so what I need for my current situation is for the "player" to always face towards the north pole of the planet. I created an empty object named "north pole" and put it at the top of my planet.

From there, I tried:

 var upRotation = Quaternion.LookRotation(player.position - NorthPole.transform.position);

I then tried to change only the "rotation.y" value of the player, hoping that this would forceably make it look towards the north pole:

 horizontalRotation.y = upRotation.y;
 body.rotation = horizontalRotation;

This did not work, the player object jerks around. How do I do this?

I need the player to continue to stand upright on the planet, but look towards the north pole always, no matter where I move him to with my mouse.

Just so you know: "player" is just a box mesh, and "planet" is a sphere mesh.