It looks like having [ShipmentNum] on the level of detail, while necessary for the path to work, is causing issues with multiple labels for each city.
I was able to get around this by creating a dual axis map with multiple mark types. The first axis I left as you had it. The second I changed to a text mark type with the city on the label and nothing in the level of detail.
Logistics-Tableau_Packaged.twbx.zip 168.9 KB
Your response was exactly what I needed, I actually didn't know you could do dual axis maps. Much appreciated!