"Should the refloat be successful, I wonder where they would take the ship for any required temporary repairs – does Australia have dry docking facilities big enough?"
YES
The graving dock at Garden island - Sydney is 1,140 ft (345 m) by 147 ft (45 m).
The MV Pasha Bulker is 738 ft (225 m) by 105.6 ft (32.2m).