Hello once again everybody.
I finally found the mistake myself. It figures that once I took the time to sign up on a forum and post it, it would finally come to me. The problem with my above code was line 19 where I created the FileWriter with the fileName string. fileName was populated using chooser.getSelectedFile().getName() which returns the naked name of the file, sans path. That is how I want the fileName variable populated, so I changed line 19 needs to the following:
BufferedWriter outgoing = new BufferedWriter(new FileWriter(chooser.getSelectedFile().getPath()));
Hope nobody has spent time on this yet!