It only took two bike rides (to a hardware store for a wee tiny screwdriver and to a music shop for a mini to RCA patch cord) and two calls to Crutchfield (one to figure out how to get my car into low gear when it’s not running so I could get the stereo out without hitting the gearshift, and one to figure out that I needed said mini to RCA patch cord).
But it is done: I have successfully installed a car stereo! I am rather surprised that I was able to do this, but quite happy that I managed to.
As promised, pictures. First, the “before” of the giant mess of my car before this started: