Okay, it was bugging me all afternoon that the circuit wasn't working - and I had a gut feeling it was my wiring, not any of the components. I was careful to identify the anode side of the diode, too... be careful about that.
Anyway, I kept looking at the circuit and then I saw my mistake. I had added the diode into the circuit but I had never connected the coil pin of the relay to the anode side of the diode... I'd left it connected straight to the emitter of the transistor. I'll have to sketch this out and figure out why that mistake kept the relay from locking, but I'll do that later... for now, I'm just happy to have figured out the error (my wiring). This is just more evidence that I need to go slower when building my circuits and check every connection in addition to checking voltage/current with my multimeter.
So, here's a video of the circuit working as it should... when I pull the magnet away from the reed switch, you'll hear the relay click once... and then no matter how many times I push the magnet back onto the reed switch, the relay will not release... it's locked.
I have to admit - it's always nice to figure out your error on your own. I'm including two close-ups of my working circuit - I'm not sure if I've made the wisest/best use of the breadboard, but hey... it works. Now I can continue with the rest of Exercise 15.