> The "Status" LED flashes some kind of code - long long, short short short. I assumed the number of flashes would correspond to the time but apparently not. We didn't have time to figure this out before we had to leave.

long-long-short-short-short is 7 in morse code. They don't say what time they tried this or if it ever changed, though, so that's just a hypothesis.

It's almost certainly this. I suspect the advance button can be used to advance the time via morse code LED flashes and only then committed when you get to the right hour.

Perhaps the long-press commits the hour, which is why it rang once initially.

I used to use Morse to blink out status codes in similar things but I think by the mid-2000s I'd moved from PIC16F628s to atmega328.

I didn't build the chime box but it looks like the sort of thing I used to do back then.