The crazy clock repo now has a total of five different firmwares from which to choose. The last one is what I believe is as close as we're going to get to Terry Prachett's vision.
This clock ticks normally, except that about half the time it will tick after 1.1 seconds instead of 1.0 seconds. Once it's gathered up 10 "extra" tenths of a second, it will instead perform a "stutter" tick, ticking twice. When it's ticking normally, the extra tenths of a second are imperceptible, and the clock's rhythm is kept undisturbed so far as can be seen or heard. But the stutter ticks utterly wreck the natural rhythm and force your brain to restart. And they come randomly anywhere from 10 to 30 seconds apart. Frequent enough to be noticed, but infrequent enough to re-establish the natural rhythm between them.
Meanwhile, the original "crazy clock" firmware seems to still lose around a half an hour a day. That's still so much that it has to be a bug. I'm going to pore over the code once more to see if I can figure out what's wrong. But while I'm doing that, I'm going to run this firmware for a while and see if it's accurate. If it is, then that at least confirms that there isn't a hardware problem (my biggest fear is that the clockwork I'm using is somehow designed to be ticked inaccurately in a particular way, which would make a custom firmware basically impossible).
If I can confirm that the hardware works, there's one more clock I might write... The Huey Clock. It will beat twice in two seconds with a heartbeat rhythm. It might wind up being to slow and boring, but we'll see.