Have never seen photo of cars using this trackage, nor read anything about it.
You would have taken a tram from the Railway Collonnade up Castlereagh Street, and it sounds as if you got off at either Market Street, or King Street. King Street sounds more likely, as it carried the city section of the Watson's Bay line until 1950, when it was cut back to Queen's Square - opposite the Law Courts and St James' Anglican Church. The Watson's Bay line then passed down College Street (the eastern side of Hyde Park), and then turned down Boomerang Street (where else but Sydney would have a street name like that?), and into William Street for the climb to King's Cross.
The connecting tracks mentioned in the original post were in Railway Square, over to the side of Central, while the Collonnade terminus of the Pitt and Castlereagh Streets lines were at the front of the station, overlooking Eddy Avenue. This line was closed in September 1957, while the rest of the Watson's Bay line was bustituted in July 1960. The Railway Collonnade came back into use as a tram terminus in August 1997 - albeit now operating in the opposite direction of travel to the original line.
Thanks Fred,I still wonder at the complexity of Sydney city tramways,the management certainly considered all their options,and when tramways in a certain area were destabilised the trams still seem to move crowds.What of the skills of connies on side steps in horror weather,rowdy passengers fired up after the sports & shows .