How to make AICharacterController able to walk on walls and ceilings?

Now that we have new NavMesh components I wanted my character to be able to climb walls and ceilings (just planes oriented at 90 and 180 degress). I can do that with simple objects, but when I use AICharacterController from Unity Standard Assets it cannot move properly, probably because of physics. I've used NavMeshLinks for moving from surface to surface properly, but once character gets to the wall it acts weird. How can I make this particular AICharacterController able to walk normally on walls and ceilings and in any orientation?

Gravity on: Character pulled down to the lower edge of NavMesh, can't move up.

Gravity off: Character moving very slowly and jittery, moves legs, sometimes "flies".

How to make AICharacterController controller (Ethan) able to move on walls and ceilings with physics normally? I've tried to add force pointing down from character model but it still didn't help. Controller doesn't move properly even when gravity is disabled in his Rigidbody component. He either moves very slow, or doesn't move his legs, or falls down, etc.

I've added this code for "click to move" in Update() of AICharacterControl:

 private void Update()
         {
             // My addition
             if (Input.GetMouseButtonDown(0) && !Input.GetKey(KeyCode.LeftShift))
             {
                 var ray = Camera.main.ScreenPointToRay(Input.mousePosition);
                 if (Physics.Raycast(ray.origin, ray.direction, out m_HitInfo)){
                     agent.destination = m_HitInfo.point;
                     //target = m_HitInfo.transform;
                 }
             }
  
             if (target != null) {
                 agent.SetDestination (target.position);
             }
  
             //My addition
             agent.SetDestination(m_HitInfo.point);
  
             if (agent.remainingDistance > agent.stoppingDistance)
                 character.Move(agent.desiredVelocity, false, false);
             else
                 character.Move(Vector3.zero, false, false);
         }