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Maybe you will be interested by the perpetual calendar patents of Ludwig Oeschlin for Ulysse Nardin.

(Note that perpetual calendars are relatively more simpler complications to design and make).

So it is possible, but hard to fit into a watchmaking piece!

The problem isn't the size of the data, it's the limits of the mechanical technology used.

I could be very wrong about this, but I suspect it might be possible to encode the data optically with much finer resolution and then contrive some kind of daylight driven optical -> mechanical transducer to extract it.

Maybe some sort of live-state electrical storage based on NAND gates, which returns a hi-low electrical value which is then read.

You guys should look at the Seiko spring drive.

http://www.seikowatches.com/world/technology/spring_drive/

Even the most snardy of mechanical watch enthusiasts agree this is a very beautiful mechanism.

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