The more difficult method would be to write something that detects serial ports like the arduino IDE and then leave some instructions for the attendant like "when starting the program each day, be sure to choose the serial port that titled 'usbmodemxxxx'" and hope that they get it right. But that just seems like such a recipe for disaster...
Only slightly more complicated than the first part of your statement is to, after you generate the list (which won't be very long), try to open each port. If successful, wait a bit (for the Arduino to reset) and then send a message. If you get the expected response, then that must be the port that the Arduino is connected to, as it is astronomically unlikely that some other device would generate the expected response. If you don't get the expected response, close the port move on to the next one.
No idiot operators were harmed in the making of the correct connection.