We start seeing them at orchid shows in January and February but mine never usually put up any flower spikes until March. This also depends upon how chilly we get during the winter months. If they don't get enough chill, they don't bloom at all for me. I even have a "heat tolerant" one that was in bloom when I got it 3 years ago, but has not bloomed since.
Your grandmother's white cymbidium is really lovely. It probably has many "children" by now. Please keep showing us your pretty flowers even though we're not being much help to your ID quest.
Melbourne is a wonderful city - I was there for 2 weeks in 1999 sailing in a big Laser regatta. Those pastry shops on Acland Street appear in my dreams still.
