Just a slight correction Nigel, it's AMSA who have the list and contact you for searching, not CASA.
There is (or was) at least 1 fixed-wing company down the road at Karratha who was Tier 4 and have been out on many searches in years gone by, along with CHC/Bristow/HeliNZ (been a while since I was around that region so things may have changed). Police Air Wing PC12 based in KA may be available too. Bond over at Barrow Island as well. There's a fixed wing charter company in Hedland and also the RFDS but I'm not sure if they've done any form of SAR work at all. Also some helos up in Broome, and some fixed wing too (Coastwatch Dash aircraft are based there).
The helos which are contracted to the offshore work up in that region typically have the ability to do winch ops, however it can take them over an hour to get the winch installed and airborne.
Someone told me many years ago even a Qantas 737, before they started their approach, went to check on a bunch of smoke that was reported offshore from KA. Someone called up thinking a boat was on fire. Was just a rig flaring!