How to prevent jitter with movement over curved slopes

I am currently building a 2D platformer where the character can walk on curved slopes.

To do this I make use of Unity's Physics with a Rigidbody2D where the RigidBody2D has the option Fixed Angle enabled. Without scripting the character will remain upright, even when walking on a slope.

To make the movement seem more natural I want the character to remain upright in relation to the ground it is standing on (in other words, perpendicular). I implement this by registering the normal in the OnCollisionStay2D event of the Character's GameObject and in then calling the following code in the FixedUpdate:

 transform.up = this.registeredNormal;

This seems to work, as my character stands up-right on any surface, but when I combine this with movement by applying force on the rigidbody it starts to jitter. Something which it does not do when I do not alter transform.up. This becomes even worse when I lerp the transition from transform.up to the normal discovered during a collision.

The code that I use to make my character stand up straight is:

 public class StandStraight : MonoBehaviour {
     private Vector2 turnToNormal = Vector2.up;

     void OnCollisionStay2D(Collision2D other) {
         if ( ! other.contacts [0].normal.Equals (this.turnToNormal)) {
             this.turnToNormal = other.contacts [0].normal;
         }
     }

     void FixedUpdate () {
         transform.up = this.turnToNormal;
     }
 }

I use OnCollisionStay2D and not OnCollisionEnter2D because I am using an EdgeCollider2D that is curved; which means that OnCollisionEnter2D will only trigger once and never again when moving over that collider.

I get the feeling that the combination of using forces to move the character forward combined with altering transform.up is a poor combination but I could not find any other way to align my character with the normal of the surface below.

Thank you for your help with this.