the 'recruitment process' page suggests that they send out paperwork to referees before they sift through the applications.
No they wouldn't.
Referees would only be approached if they were going to offer you the post.
HR and the ATC General Manager will have done a paper sift of all applications by now, it's just a question of them getting together to decide upon who they're going to put under the thumbscrews at interview.
Having worked at airports and in ATC for a long time, I know how painfully slow the process can be but stick in there folks and good luck to you all.