Edit: I think I figured it out. I'm using a plastic TO-92 transistor, where the pins are number 1 (emitter) to 3 (collector) from left to right, and got the emitter and collector mixed up. On the original metal can version, the pins are usually shown 3 (collector) to 1(emitter) from left to right. No excuses, but that's why I was so confused, and why my hand-drawn circuit looked backwards. My circuit is actually exactly the same as the "switch" version shown above, and works fine that way. And, as predicted, I'm seeing that lower resistor values on the voltage divider create sharper on/off transitions. I'd still like them to be sharper still, but it's useable now.