Plus side: got the thing completely drained and flushed, and refilled, and we'll see if the water was stinky because of sediment. I hope so.
...and I found, next to the water heater, what looked like an unused anode. So I don't need to go buy one; and in fact if I could just get this one out maybe it would turn out not to need replacing. But I don't know, and that's the problem.
Anyway, we'll see how the water smells tomorrow, I guess. Crossing fingers that it was just because of sediment....