I wonder if there are there any markets anywhere in the world where company shares are publicly traded, valued by a quantitative means, such as a multiplier of revenue or profit?
So the answer to your question must be no, there are no stock markets where shares are traded on a purely quantitative base. This is because the only way for price discovery on such a market is by perfectly predicting the future, which is not (as far as we know) possible.
I don't think reported actual figures are enough to form a good enough image of the worth of a company. The proverbial example would be of buggy whip companies (selling whips for horse drawn carts) reporting record profits the year that Ford opened his first automobile factory. Clearly the buggy whip companies did not have a bright future ahead of them, but you wouldn't be able to tell from reported figures.
Overvalued is in the eye of the beholder, in this case the market. There were people willing to buy the stock at that price, why not sell it to them? If the buyers really believed it was going "to the moon", then you could just as well argue they cheated a lot of potential buyers out of the chance to get in on that action.
Finally, if you do think it's overvalued, arguably the best thing to do as a company is sell more stock, to maximize the amount of money per share you get. This is the way Tesla does it for example: they only sell more shares into the market when the stock price is particularly high.