We fixed basement lights!
Dad came over, and, after a bit of difficulty tracing back where electrical cords went, leading us to simply decide to turn off ALL power to the house just to be on the safe side, we worked on the lights that were out in the basement.

As it turned out, we didn't end up having to turn off all the power; we were able to trace things back enough that we just turned off power to the first and second floors, and SOME of the power to the third floor. . .

However, once we did that, it was EASY.

Replacing keyed porcelan light fixtures is dead simple. See, because it's "replacing", the box the lights are installed into is already there. So you unscrew the broken fixture from the box, detach the black and white wires from the back of it, and throw away the broken fixture. Then you attach the black wire to the dark screw on the new fixture, and the white wire to the light screw on the new fixture, and you screw the new fixture into the box. That's it. It takes like five minutes -- once you've managed to find and turn off the power, that is. . .

There's actually a significant subset of electrical work which consists basically of "turn off electricity. Connect black wire to dark screw and white wire to light screw. Turn electricity back on." I feel reasonably competent to handle that subset.