Applying twice for the same position
Technically, I cannot change my application documents any more or withdraw my application through the website of the hiring department.


Says who? Did you talk to a real live person about this? It's quite possible they can accept an "overwritten" re-application even if the public web interface, or what-not, doesn't support this.


  The best I could do is submit a new application using a new e-mail address.


Not so. You can write a letter, explaining how you understand that the department's hiring focus is Y rather than X, while your earlier application emphasized X, and asking the application reviewers to consider an enclosed summary of your activities and plans regarding Y.