The PCBs I had printed up finally arrived!
Took a little longer than I expected to get it all soldered up (so many wires!), and the fact that the screw terminals I bought are junk didn't help (about 1 in three had screws that seemed to be cross-threaded and of course I didn't realize this until AFTER I had soldered them to the board). But now it's nice and tidy and I shouldn't have to worry about any wires popping loose off of the breadboard.
I also added a track of the theme music to the SD card, and adjusted my code such that it plays whenever the button is pressed (Found out the other day that my 1-yo daughter LOVES the song, so now it's always a button-press away).
I've also since added a magnetic sensor to a window that's by Hal, that I use for other automations in my house (specifically to alert me when the outside enthalpy is lower than the inside, I'm not in heating mode and the window is currently closed). No other sensors currently planned, so I THINK this project is finally all done...