I can import or export. But my refineries and oil wells simply won't deliver to the trade port, only trade depots.
Based on some of the issues seen for recycling centers that all of the buildings of a particular type are grouped together as one controller/scheduler. Therefore all of the coal mines on the map will send their loads to a single trade depot/port until its full and then move on to the next one. This makes it incredibly difficult to shut down older trade depots (as 'accept local deliveries' is sometimes ignored and/or what's on hand won't get exported as all of the trucks are swarming another depot. IMHO if you want the port to be used you'll have to nuke the trade depot (you won't have to keep them once the port has been unlocked).