Aligning a rigidbody smoothly with the perpendicular of a vector angle

So I've been struggling a number of hours on this one (however, most of that was due to the fact that I didn't realise Atan2 existed). Anyways, my goal is to be able to keep a rigidbody perpendicular to the vector angle of it's Z-axis, in a way that looks smooth. Particularly, I'd like to be able to change the rigidbody's z-rotation at a rate proportional to the distance between the current z-rotation and the vector-based angle. The end effect should be able to let a player go around a loop (if they have enough momentum) and keep their feet to the floor (think Sonic the hedgehog).

Here's what I have so far (in C#):

     public void adjustZRotation(float xVelocity, float yVelocity){
         
         Vector3 newPosition = new Vector3(transform.position.x, transform.position.y - 1.5f, transform.position.z);
         
         //Don't change Z Rotation if there is nothing 1 unit under the player (linecast starts from the middle of player)
         if (Physics.Linecast(transform.position, newPosition)){
             
             //Get the angle (in degrees) of the combined x and y vector.
             float zAngle = Mathf.Atan2(xVelocity, yVelocity) * 180/Mathf.PI;
             
             //Make zAngle represent a full positive 360 degrees
             if(zAngle < 0){
                 zAngle = -zAngle;
             }else{
                 zAngle = 360.0f - zAngle;
             }
             
             //If the player's vector-based z-angle is the same as their real rotation z-angle, then do nothing.
             if(zAngle == transform.eulerAngles.z){
                 return;
             }
             else{
                 //Set the new Z-axis rotation perpendicular to the zAngle
                 transform.rotation = Quaternion.Euler(0, 0, zAngle + 90.0f);
                 
                 //If possible push against the zAngle for a more gentle change.
                 
                 //###Currently overshooting desired results###
                 //if(transform.eulerAngles.z > zAngle){
                 //    Quaternion deltaRotation = Quaternion.Euler(new Vector3(0, ((transform.eulerAngles.z - zAngle) / 2), 0) * Time.deltaTime);
                 //    rigidbody.MoveRotation(rigidbody.rotation * deltaRotation);
                 //}
                 //else{
                 //    Quaternion deltaRotation = Quaternion.Euler(new Vector3(0, ((zAngle - transform.eulerAngles.z) / 2), 0) * Time.deltaTime);
                 //    rigidbody.MoveRotation(rigidbody.rotation * deltaRotation);
                 //}
             }
         }
         
     }//adjustZRotation

Unfortunately this function doesn't work quite like I'd like. It does keep the rigidbody perpendicular to the angle I want, however it is extremely rigid (no pun intended) and a bit fidgety (although some of that is due to the linecasting I do).

So the question is: Is there a way to do this smoothly? Or am I going about this the wrong way? I added some of my experimental code as a comment, but in it's current state it often rotates the rigidbody too much or too little. On a positive note rigidbody.MoveRotation does seem to take care of the smoothness issue.

Thanks for everything!