This is still a misunderstanding of Menger. Menger's argument is
not that societies were organized around barter at all.
He argues that where barter exists, people will quickly converge onto one or more forms of money for organizing trade. Even if it is not the intention of individual tradesmen, some astute traders will realize that they can profit by matchmaking (a necessity when there is a double-coincidence of wants). These astute traders will pick commodities which have the best saleability (those which are mostly likely to be accepted in exchange for other goods, and which retain value) as their means of measuring trade value. The successful traders will in turn, define which commodities emerges as the common monies in that economy, because traders who chose other (less saleable) commodities as their unit of measure will not be as successful.
It is not surprising that there are no historical documents outlining this, for it would likely pre-date even the written word by centuries or millennia. If it were the intention of a matchmaker to profit from establishing trades through use of goods with high saleability, they would also not likely advertise their tactics willingly, as they would be in competition with others attempting to make similar trades.
There are many historical accounts of monies being displaced when new, superior forms of money enter into economies, which is an extension of Menger's thesis (Also known as Thiers' Law). If a society is using a form of money which for whatever reason becomes much less saleable, and a new commodity enters the market which is more saleable, the more saleable commodity will eventually displace the old money.
So if it were the case that silver was selected (by who?) as the first money, 'for reasons', it seems like they hit jackpot on first try, for silver would remain the most saleable commodity for millennia until it would be later displaced by gold. Call me sceptic, but I don't buy such coincidences.