I have learned an incredibly valuable lesson, and that lesson is: I do not like soldering prototypes on perfboard. I was at it for about eight hours spread out over the last few days, and in perhaps the fifth hour I paused to reflect on how much time I was putting into cutting, stripping, routing, soldering, and checking connections. I thought about how, these days, it only costs $75 to get a batch of 4 or 5 PCBs made and shipped to your door, with just a week of lead time or less. And finally, I concluded that doing perfboard prototypes is for the birds. Next time, I'm just going to get PCBs made at a board house. Eight hours of my time is worth more than $75.
This time, I powered through my prototype anyway. It's not the prettiest thing in the world, but it works! This is the first (and will be the last) time that I've tried using copper tape as ground and power bus. I'm not convinced the benefits outweigh the complications.
I might get a batch of PCBs made for fun, anyway, but if I do I'm going to shrink the design and use a bare ATmega32U4 instead of a Teensy.