Moving Character Along Round Tunnel Walls

What I'm trying to achieve is to align and move character inside a (arbitrary shaped, yet round, twisting and maybe looping) tunnel shape with "feet" always touching the ground. Physics and path following are not options for me, so I started with basic raycast solution:

 void Update()
     {

         RaycastHit rcHit;
          
         Vector3 theRay   = transform.TransformDirection(-Vector3.up);
          
         if (Physics.Raycast(transform.position, theRay, out rcHit))
         {
             float groundDis = rcHit.distance;
 
             transform.rotation = Quaternion.FromToRotation(Vector3.up,rcHit.normal);
             
             float movement = Input.GetAxis("Horizontal") * rotationSpeed * Time.deltaTime;
             
             transform.localPosition =
                 new Vector3(transform.localPosition.x + movement, (transform.localPosition.y -  groundDis)+.2f, transform.localPosition.z);            
             
         }
     }

However the result is not what I expected. At first everything goes smoothly but when character has moved enough to left/right so that he's standing in angle of >90 degrees sideways he starts going through the tunnel wall, eventually going through the wall and preventing raycast from hitting the wall.

What am I missing here? Does someone have a better way of doing this?