You mention of the parameters being sketchy for the day. What do you feel was lacking in this storm outbreak?
For most of the big storm days in Australia, there always seems to be something missing. Probably fair to say that moderate to high CAPE with strong deep-layer shear is not exactly rare. These conditions are favourable for supercells with very large hail. The low-level shear is however, usually quite weak and LCL's too high which probably explains the lack of tornadic storms.
I thought I would bring up the September 2009 duststorm too since that was quite an interesting event. Here is the Woomera sounding-
The wind profile on this sounding is quite amazing with an 80 knot NW'y at 500 mbar and a 50 knot NNW'ly at 850 mbar. Mid-level lapse rates are also very steep (though the 300 mbar temp is a bit warm in this sounding). The biggest problem though is the low-level moisture. The surface dew points were only in the low teens that day in the warm sector so instead of a tornado outbreak we had a dust storm.