"Chasing" object around a sphere

Hey all,

For a project, I've got planet-based combat as part of the gameplay. In short, I use forward movement and rotation followed by rotational and positional clamping to the planet's surface. It uses a bit of spherical coordinate math, but that's not important.

So, I have enemies that I'd like to follow my position, wherever I am on the sphere. This, however, is proving difficult. Using transform.LookAt(player.position) only works well when they're closer on the sphere, but farther away, and I get a quasi-Gimbal Lock scenario.

What's the best way to have something rotate so it's forward vector propels itself toward an object on a sphere? Thanks in advance!

Also, here's the code, so you get an idea of what I'm doing to "clamp" it and such.

 // Applies yaw changes (DOESN'T WORK RIGHT :C)
 transform.LookAt(player.transform.position);
         
 // Applies forward movement
 currentSpeed += Time.deltaTime * enemyPlanetAccel;
 currentSpeed = Mathf.Clamp(currentSpeed, 0, enemyPlanetMaxSpeed);
 currentSpeed -= Time.deltaTime / 2f;
 transform.position += transform.forward * currentSpeed * Time.deltaTime;
         
 // Correct turns/position to limit to planet's surface
 Vector3 c2s = transform.position - planet.transform.position;
 Quaternion newTurn = Quaternion.LookRotation(Vector3.Cross(transform.right, c2s), c2s);
 transform.rotation = newTurn;
 transform.position = sphericalToCartesian(new Vector3(landingRValue, cartesianToSpherical(transform.position).y, cartesianToSpherical(transform.position).z));

Thanks again for any help! :)