I would think it would just be easier to use Club/Biz check-in and South fast track security for all of you. I have the feeling that since the First Wing opened, the reduced number of people going through south fast track makes it a breeze to use. But that is admittedly based on limited experience since I am usually on AA out of T3 to the US and only use T5 south when I have to overnight in London on the way back to Croatia.