Mentioned by Joe Rose:
We're working across the two layers here.
One boundary segment is assigned a "Master" roll. In this case the county (blue line).
Selected vertex reference 1 is master start point.
Selected vertex reference 2 is master end point.
Selected vertex reference 3 is slave start point.
Selected vertex reference 4 is slave end point.
Now starting a #1 bring # 3 to that point
Continue to the end points as required.
One of boundary segments can have more/less vertices than the other. So the slave must have residual points removed or deficient points added as required. Now the slave is matched to the master and can be saved.
Now we have this (which I had to do manually):