The amount of scholarly evidence backing a “weight” or mass of the ancient shekel based on the evidence of hundreds of perfectly preserved (read: having resisted entropy) balance-pan scale weight in the vicinity of 8.3–8.4 grams is overwhelming. The methodology used and the results are here:
Weights, those calibrated stones and metals used in balance pans, have implications for many socio-cultural processes…www.academia.edu
Balance pan weights are used in both manufacture and trade and therefore are a correlate of economic activity. Ancient…www.academia.edu
While it is well known that at other times and places the shekel had widely varying values in mass, your un-referenced assertion of a different “weight” for the period in Ancient Sumeria you describe in your essay seems to be grossly inaccurate. Also inaccurate is your assertion of a “gold” mina which exists nowhere in the archaeological record of the ancient period you cite.
Also, even a non-geologist understands that the relative abundance of the precious metals distribution in the lithosphere from one place to another is incomparably large. Ancient Egypt is known to have exchange gold for silver on a one:one basis, and there are many scholarly references to a view of gold in Ancient Sumeria that seldom rises above its decorative utility — certainly no indication of a monetary use until many centuries after the period you cite.
A mina of ~504 grams derived from 60 shekels of 8.4 grams each is much more consistent with the empirical record.