I just finished up the rest of the project- at least pretty close. I etched the and assembled the second board (this one with red LEDs), and stuck it in its case. I also added a cap screw to each of them, approximately where the winding knob would be on a real pocket watch. This is partially for aesthetics, but it also serves as a way to attach a chain, if that's desired in the future.
I've also made a couple of tweaks that have definitely improved the performance. First, I lowered the op-amp's gain to around 1/4 of what it was initially. I finally took the time to look at the wave on a scope, and it was clipping even when I played notes at moderate volumes. It will still clip now if I play loudly right into the mic, but I'm calling it good. I'll consult my friends after giving it to them to see if it works for their use case.
The second change I made was firmware. The micro I'm using (barely) doesn't have enough RAM for a 512-element FFT, so I was using 256 elements. I then occurred to me that the performance hit for using things other than powers of 2 might not be so bad, especially if it gains me something in terms of accuracy. Well, I upped it to 384 elements (one power of 3 in the FFT, so probably not a huge deal), and it seems to have improved things nicely with minimal processing time increase. At least I don't see any great change.
The "(ish)" part of "Done(ish)!" concerns the little things- final tweaks to the gain, playing with the sample rate, expanding the range of notes the device will detect, etc. It's good enough right now that I'd be willing to give it to my friends and not be embarrassed about it, though.
And because everybody loves pictures, a couple more:
Showing both of the completed Pokey Watches.
Same thing, except from the front. You can see the cap screws a little better here.
The awesomely-obnoxious green charging LED. I actually like it... it produces kind of an alien effect when the watch is [almost] closed.
Anyway, I'm marking this as "done", despite the potential for future tweaks.
Oh, and I realize that the Git KiCad files are broken (missing schematic libraries). I'm getting to fixing it sometime. The layout should be usable, though, and the code is all set.