A fired clay would dry fairly quickly I would think (though probably crack), but twisting a rod makes sense given the urgency!
Many theory's exist as to its place of origin, the Antikythera device but its destination would likely have been Rome for Julius Caesar.
I think everyone was surprised at the complexity of the device for its time, though confirmed the gear train is not as complex as originally thought, just one more gear missing as far as I'm aware. I remember reading someone originally thought it must be some sort of mix up with the museums artefacts dating it much later. I dont know that much about it but given a nation of scholars together with the Greeks interest in astronomy and mathematics, its was possibly made as a teaching device and more than likely made by several contributors?
My mate Leo, job title; painter, inventor, sculptor, architect, mathematician, musician, engineer, anatomist, geologist, cartographer, botanist, and writer.- a chronic procrastinator and a sure sign of a genius if ever there was looking for perfection!
Actually he conceptualised a lot (multi-talented do tend to theorize more than do apparently), I blame his employer Ludovico for running him ragged for years, yet its strange given your example of the Greek astronomical devise and what they were able to acheive, that it has been suggested many of his designs weren't constructed because of technological constrains, far, far ahead of his time as it were but we do now know that he invented the helicopter and a tank! also many more of his designs were never published/realised or saw the light of day, unlike the automated bobbin winder and other easily crafted designs, and he was also the guy to design the device for testing modern day breaking strain of monofilament fishing line! :w
Okay I made that last bit up, but he did invent a machine for testing the tensile strength of wire...
What comes close, well nothing much predates that Greek device does it Mark? but I know what Ron Clay would say.... Tesla and who could blame him for saying so, another genius ahead of his time - the inventor of 'wireless communications' and AC current!