I've reached a great milestone tonight. For the first time, I'm actually sending data to the keyboard using the real communications protocol. I wrote a very simple demo program in AVR C to show off a few LED patterns and beep the speaker a few times. Video embedded below.
Now that I know the circuit works, I'm in full AVR C programming mode. Best of all, because the clock is fully implemented in hardware, I don't have to spend all my time worrying about tight timing conditions. I'll be pushing my code on Github just as soon as I remove some of the more embarrassing comments!