Well, I loaded the "alpha" firmware, temporarily connected the keyboard, and fired it up. No magic smoke was lost (not that I was expecting any, since the board worked fine with the LUFA joystick demo), and it enumerated as a keyboard.
I pressed the low "F" key, and… I GOT A KEYSTROKE! Of course, it was the wrong one… but, hey, at least it's something, right?
It turns out I somehow got the key-map "end-for-end", despite drawing a really nice diagram of the rows and columns. Something slightly more odd is the fact that each "row" is rotated one "column" to the… left, I think… yeah, left. I'm assuming this is a software problem, since the matrix is very straight-forward, but I can't figure out why it's happening. Once I get the source posted, I'd appreciate some more eyeballs seeing what I'm missing and letting me know about it.
First, though, I have to get the keys properly connected to the board. I've ordered some single-row, male headers from fleaBay. I'm going to replace the tiny piece of ribbon-cable on the keyboard with a longer one from an old floppy cable, and put some pins on the other end. I'm going to put another set of pins on the AVR board. Then, I'm going to plug both sets of pins into a breadboard socket. Easy-peasy. They're estimating Thurs. for delivery of the headers, so I guess I'm on-hold until then (which will give me time to github-ify my code, and maybe post some pictures).