After a drive down to Canberra and back with my father and step-mother, I finally have my visa! A big thank you to the visa unit staff who took pity on me and put my visa into my passport on the same day - Australia Post probably wouldn't have been fast enough for me to make my (already delayed once) flight.
We were in a bit of a rush when we lodged the original applications in early December, as they'd been delayed by my need to get a new passport - the old one would have expired half-way through our stay in the UK - and a trip to Vietnam and Cambodia. So I checked the forms repeatedly, but forgot to check the documentation showing that C and I had been in a "marriage-like relationship" for two years... So my initial application (as the unmarried partner of a Tier 2 Skilled Migrant) was rejected and I had to lodge an appeal, with extra documentation. This took nearly two months to come through, which meant I had to delay my flight and couldn't travel with C.
The moral of the story? Don't rush your visa application, as getting it right is almost always going to be more important than getting it done quickly - and initial applications are processed much faster than appeals.
Also, Australians should note that "de-facto" status doesn't exist in the UK. When you've been together for seven years and live in a country where de-facto relationships are ubiquitous and treated pretty much like marriages, it is easy to take your partnership status for granted. Proving that in a legal context where there is no status in between Single and Married ("Civil Partnership" is only possible for gay couples) is another matter entirely.