I will add a few things here. From what I understand, the temperature/dew point at Taree was 26/22 at 1200 EST. Taking a surface-based parcel of 26/22 from the surface and lifting to 500 mbar gives a temperature of -4/-5. The 500 mbar temperature on the Williamtown sounding was -13. Therefore, a rough estimate of the surface-based lifted index (LI) would be around -9/-8. Using a surface-based parcel instead of a mixed-layer parcel usually gives an overestimation of the instability. However, given the direction of the lower-level winds in the afternoon and the observation of scud cloud around the time of the Bulahdelah tornado I would think that moisture would have been quite “deep” in the afternoon. Also, if the observation of 26/22 was taken at midday then there may have been some further heating during the afternoon.
Taking a look at the upper wind profiles from Williamtown and Coffs Harbour in the afternoon, a couple of things are quite interesting. At Coffs Harbour, the lower-level winds are extremely strong and turn from NNE to NW. This would give an enlarged hodograph with strong anticlockwise turning favouring left-moving supercells. The only flaw with the Coffs Harbour upper-level wind profile is the relative weakness in the 700 to 500 mbar winds (40 to 45 knots, not much of a flaw really). The wind speed at 500 mbar at Williamtown is very strong at approximately 65 knots. However, the lower-level winds are not as strong as at Coffs Harbour. For example, the 850 mbar wind speed is only 20 knots from the NE (still pretty good in Australian standards). I wonder whether between Coffs Harbour and Williamtown there was a blend between these two upper-level wind profiles giving both strong lower-level and mid-level winds. If so, that would be a near-perfect profile for strong to violent tornadoes given the strong instability and low LCL’s present that day.