Good to get you conclusions Keith (if I may), we agree on the main outlines.
 I would add that many people ran quite active pre-coinage markets in the
historic period – the Akan using gold dust in 19th century West Africa, the
9th century Vikings using silver (and probably copper) bullion, the 18th
century Burmese using base metal bullion etc.  The pre-Columbian Mexicans
apparently ran very active markets (primarily using cocoa beans as currency)
and there are wall painting from Ancient Egypt which appear to show market
stall holders.  Thus I find it entirely plausible that such activities had
their roots lost in the mists of time, in the Neolithic if not the Palaeolithic.

That is to say,  Polanyi too was involved in spreading a lot of nonsense.

We also agree - the change - from markets being a subsidiary mechanism for
distributing goods to being the primary mechanism, is coins.  Coins fuelled
the rise of more meritocratic and thus more productive societies.  I would
add two other hot spots where coin using polities arose early on, aside from
the Aegean - North India and China..   I would further add I see it as a
mistake to think of coins being invented.  The idea of coinage was too
simple to need any inventing.  It is rather a matter of people being allowed
to have them (this in line with Leslie Kurke)

The big puzzle here, it seems to me, is why has this very obvious story line
been so frequently and thoroughly suppressed?  The story of this suppression
is itself ancient.  Coins use seem to appear in Lydia around 610BC, and
spread like wildfire, arriving in Athens about 550BC, and apparently
transforming Athenian society.  Yet, as Kurke points out nobody even
mentions coins exist in any text until about 460 BC.  The principle players
in the rise of coin issue were apparently the early tyrants, the
intellectuals associated with their early use the sophists – yet both
"tyranny" and "sophistry" had gained pejorative overtones even in the
ancient period.

More accessible is the suppression of this story over my own lifetime.  If
the most obvious story line is true, then the early tyrants seems to have
created something very like a social contract with their subject
populations. It ran – ‘I give you coins, and allow you to spend them at
markets, you use them to pay taxes, with which I defend the state, and
police the markets etc’.

But anyone adopting this story line even today runs up against those aligned
with Polanyi, who dislike, even detest, markets, and simultaneously, those
aligned with Hayek, who very often clearly detest the state.  Thus if one
argues that modern markets were deliberately created by states, issuing
coins, one will get shot by both sides.  (As kids say today, “Been there –
got the T-shirt”.)

I will check out your book – sounds good.  Have you looked at Sitta von
Reden's 2010 parallel publication?  (‘Money in Classical Antiquity’)  On pp
10-11 she seems to me to be locating Moses Finley rather firmly in a
specifically cold war context.

Rob Tye, York, UK