I found a (Japanese-language) report about the clock mechanism, with some interesting photos. From context, I'm guessing this is a product of the 2004 reverse-engineering program described in OP. For example, page 4 has a photo of the (very weird) gear OP describes as "rhinoceros beetle" shaped, with the modern replicas next to it.
Masahiro Kikuno, a Japanese independent watchmaker, made a single piece [1] of a wristwatch design that displays wadokei time for a contest. I wonder if he used a similarly shaped gear, and can only imagine his piece (made in 2011) was inspired by the 2004 reverse-engineering of this clock.
The National Museum of Nature and Science in Ueno Park, Tokyo is my favorite place to visit in Tokyo. Everytime I am in Japan I'd find time to visit it. Its 630 yen entrance fee is a steal. I can spend a whole day in it, alongside school kids on field trip.
It is staggering that he made the machine so efficient that it could run a full year on a couple of springs. They aren't even gigantic. And this is with hand built everything using 19th century metallurgy. Just phenomenal.
Never underestimate the amount of stored energy in a coiled spring... but I think the long runtime can be attributed more to low friction --- if the gear train is well-balanced, and bearings sufficiently well-polished and lubricated, then very little energy is required to rotate it.
The wadokei mechanism reminds me that before electronics, to automatically turn lights on and off at sunset and sunrise, mechanical "astronomic timers" were used; I believe they don't use beetle-shaped gears, but instead cams, and are adjustable for the latitude.
I recently got to tour the Toshiba Science Museum where the replica is running.
One of the employees checks the clock "about five times a day" when he's working. He checks the accuracy of the western style clock and the humidity in the glass case in which the clock is housed.
I don't recall at what percent they keep the humidity, but they have packets hidden under the clock which release moisture and absorb moisture as needed from the air in the case.
Pendantic language question: The clock's Japanese name is "万年自鳴鐘" per the article... Then they say "Literally translated as the 'million year clock'"... But they also call it the myriad (10,000) year clock... (And 万 is 10,000, right?)
As a result, even though 万 literally means 10,000, it is possible that 万 is used as more of a general idea for longevity. However, the article using the world "literally" would still be incorrect, I suppose!
Anyways, just figured that might clear up a small part of your question, since the usage of 万 is not necessarily literal in many East Asian languages.
万 is 10.000 but often used similar to how we use million to denote "a large number" (as in "one in a million chance", which doesn't mean literally one over a million, it just means really small)
I can only imagine all these language had a word for 'uncountable number' which was then repurposed as mathematics developed (you need to invent column placeholders and powers of 10 before you have a specific notion of '10,000')
億 is just 10,000 * 10,000, perhaps you could say "a myriad of myriads" if one myriad wasn't enough.
Wikipedia article on 10,000 has this to say:
Many languages have a specific word for this number: in Ancient Greek it is μύριοι (the etymological root of the word myriad in English), in Aramaic ܪܒܘܬܐ, in Hebrew רבבה [revava], in Chinese 萬/万 (Mandarin wàn, Cantonese maan6, Hokkien bān), in Japanese 万/萬 [man], in Khmer ម៉ឺន [meun], in Korean 만/萬 [man], in Russian тьма [t'ma], in Vietnamese vạn, in Thai หมื่น [meun], in Malayalam പതിനായിരം [patinayiram], and in Malagasy alina.[1] In many of these languages, it often denotes a very large but indefinite number.
I assume the author means creators of typeset, though I'm unaware of this usage and it's amusing to imagine a bunch of poets quixotically and inexplicably employed in fine metalworking for an exquisite clock :D
[.pdf] https://www.global.toshiba/content/dam/toshiba/migration/cor... ("万年時計の機構解明 Mechanism of “Man-nen dokei,” a Historic Perpetual Chronometer")
(I'm fairly sure no English translation of this document exists anywhere, at least indexed on Google).