Google Maps Drawing Tools: Route path between points using Directions API

Question

This is sort of a follow up to another question I asked that didn't get any answers. I've done more research and figured out pretty much what I need to do, but unfortunately I can't figure out HOW to do it.

I have a map with Google's Drawing Tools set up. Users need to be able to draw a polygon to define a delivery zone. With each new point added to the polygon (before completion), the line should automatically follow roads on the map to get from the previous point to the new one. The result should allow lazily-drawn polygons to match roads exactly, without all the effort that would otherwise be required.

Here is my in-progress Codepen

I had it working before with the Roads API snap-to-road feature, but found that it wasn't nearly accurate enough. I need paths to be drawn from a very far zoom level and still snap to whatever roads they can find.

Here is the most relevant function which should run on every new point's creation (right now it's attached to the polygoncomplete event since I haven't figured it out):

function runSnapToRoad(poly, path, color) {
  console.log('Run snap to road');

  var pathValues = [];
  for (var i = 0; i < path.getLength(); i++) {
    pathValues.push(path.getAt(i).toUrlValue());
  }

  service.route({
    origin: path.getAt(path.getLength() - 1),
    destination: pathValues.join('|'),
    travelMode: google.maps.DirectionsTravelMode.DRIVING
  }, function(result, status) {
    if (status == google.maps.DirectionsStatus.OK) {
      for (var i = 0, len = result.routes[0].overview_path.length;
          i < len; i++) {
        path.push(result.routes[0].overview_path[i]);
      }
    }
  });
}

In short, my question is as follows:

How do I get the previously-added point and the most recently-added point of an incomplete polygon, and use them as the "origin" and "destination" for the Directions service?