Show me a pairing that requires more than 5 shirts. Even on 418 you get by with 5 shirts as the SYD-CHC-SYD is a turnaround.
Ok, so you found one pairing that requires 6 shirts. So how often do you get that? Just have one cleaned at the hotel for a couple of DHS and in that case claim it back if you are that thight on the money.