So, why did I make such an egregious error when designing revision 5B boards?
Because the TinyFPGA BX project has (or, at least at one time, had) poor revision control and misleading or missing documentation.
When I was building revision 5B, I was working off of this photograph, which is one of the only documented listings of the I/O pins accessible on the underside of the TinyFPGA BX module. (If you can find an official description of those connectors on the https://tinyfpga.com website, please send me the link!) Observe the bottom "belly connector" (what do you call those things anyway?) is a 2x7 surface mount connector, which lines up with what I've built the 5B to work with.
However, if you look at the current OSH Park PCB artwork, you'll see that there's a 2x8 surface mount connector in its place. This matches up with the actual hardware I tried using to build the latest prototypes with. As far as I can tell, it looks like the exact same pin-out as the 2x7 connection, but with an extra pair of ground pins.
Of course, looking at the schematic, I see that it describes the 2x8 connector; but, considering the Crowd Supply updates are newer than the schematic up on Github and showed the 2x7 connector, I didn't put much stock in trusting it.
Turns out, Crowd Supply's information is outdated. And, strangely, I can't even find reference to the 2x7 connector in Github's history, suggesting that the CS campaign started before the Github repo even existed.
So, yeah, I learned a lesson on this one: never trust the updates on Crowd Supply. Even if newer than repository documents, they may not reflect current reality.
OK, back to hacking on the next PCB revision.