There is no 9–6 overlap. Stretching to 07:00–21:00 on both sides gives you 16:00–21:00 Chicago time:
16:00 you → 07:00 Sydney next day
17:00 you → 08:00 Sydney next day
18:00 you → 09:00 Sydney next day
09:00→00:00next day · outside Sydney working hours
10:00→01:00next day · outside Sydney working hours
11:00→02:00next day · outside Sydney working hours
12:00→03:00next day · outside Sydney working hours
13:00→04:00next day · outside Sydney working hours
14:00→05:00next day · outside Sydney working hours
15:00→06:00next day · outside Sydney working hours
16:00→07:00next day · outside Sydney working hours
17:00→08:00next day · outside Sydney working hours
Working hours assumed 09:00–18:00 local. Offsets include daylight saving where it applies, so this shifts through the year.