This is an old post, preserved for reference.
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Whilst I'm waiting, here's a look inside the original 30 year old clock.
Inside there's a lot of space where the radio used to live.
It's a three board construction
With one for the top buttons, one the logic board with a single IC and finally the display
The chip is a TMS3450NL, and the date code (32nd week of 1983) seems to fit with the 30 year old estimate.
I have managed to find a scanned datasheet for the chip:
After all this time of putting up with a 12 hour clock, I find that not only did the display have sufficient segments to display 1 and 2 (but not 8), the chip supported 24 hour mode, it just needed a pin shorting to ground.
On to part 3 - more on display multiplexing.