How to get a "Traveled" vector point along a path with some width?

For example I have a path, that consists of 10 cross sections. Each cross section defines a center point and edge points. So in total I have 30 vector points that define my path, which the traveler X can travel. My goal is to receive the traveled distance along the center points, centerpoints[currentPoint].

My current approach relies on dot product, but as soon as the traveler goes away from the center I get incorrect results. I am currently not using the edge points, but they are there if needed, because they define the width limits to the path.

Here is the code of my approach:

         int points = 10;    // size of the path list
         int pointNumber = 0; // find the closest point in path list to traveler
         
         // Measure the total length of the path and store distance per segment
         float accumulateDistance = 0;        
         for (int i = 0; i < path.Count; i++)
         {
             Vector3 p1 = path[(i) % points].centerPoint;
             Vector3 p2 = path[(i + 1) % points].centerPoint;
 
             if (p1 != null && p2 != null)
             {
                 accumulateDistance += (p1 - p2).magnitude;
                 path[i].dist = accumulateDistance;
             }
         }
         
         // Measure the traveled distance along path
         Vector3 currentPoint = path[pointNumber].centerPoint;
         Vector3 nextPoint;
         if (r.currentWaypoint < path.Count - 1)
             nextPoint = path[pointNumber + 1].currentPoint;
         else
             nextPoint = path[0].currentPoint;
             
         Vector3 forward = (nextPoint - currentPoint);
         Vector3 relativePos = traveler.transform.position - currentPoint;
 
         float distAdd = Vector3.Dot(relativePos, forward.normalized);
         progressDistance = path[pointNumber].dist + distAdd;