My bad- I checked it again today, and it actually says "unlocked". The hazard switch on the left is a true toggle, but this functions as a radio button and the light comes on when it is clicked. When I clicked it, I thought I heard a sort of vacuum hiss from the engine compartment, but it's hard to tell over my exhaust leak :-(.

Now I'm completely lost again. This implies something is locked by default and needs to be unlocked everytime the car is started? A differential wouldn't be set up like this, would it? What else could it be for?

Thinking more about it, I'm not sure if I regained traction while cornering because of a LSD, or my instinct to ease off the gas until the wheel stopped slipping. Is there a simple way to determine the differential type without damaging the underbody?