I am speculating here. This is for research inspiration, not the result of research.
The data you mention seem to indicate two trends. One is tanki versus dam, the other copper versus silver. The tanki versus dam trend is a traditional versus a new-fangled coin and a political issue. The moguls would have liked the dam as a common unit in all their lands, the traditionalists (clergy and small shopkeeepers) would have gone with the tanki. The shroffs would have wanted both in order to profit from changing one for the other. The variables would have been the strength of the moguls, the preferences of the governor and the political stability of the population inside Ahmedabad. Remember that Akbar once said he'd conclude a treaty of friendship with any ruler who would accept his standards.
The other trend is economic in nature. If you have coins of two or more metals circulating at a fixed relation, you need to change the weight relation if the price relation changes, unless you have built in a safety margin in that the coins of at least one metal are grossly overvalued (underweight). The relation can be changed by adjusting the coins of either metal. Making the undervalued coins heavier will result in deflation (prices going down) and an appreciation of the currency on the export market. Making the newly overvalued coins lighter will induce inflation and a depreciation of the currency. In both cases, old coins should be counterstamped and their value adjusted to prevent Gresham's law from kicking in.
What is in the above paragraph is factual, not speculation. Some international examples may be useful. Keep in mind that price stats are rare. Numismatic research should produce a long series of rice prices.
China. Cash coins were standard and seriously underweight, but their weight was changing. Not as much as the price or weight of silver ingots, though. Foreign merchants got shocking profits out of silver, because the government stuck to a fixed relation between silver and gold. This also led to the Spanish colonial pesos being accepted.
England and the UK. Copper was generally underweight, sometimes (Ireland!) shamefully underweight. There was a flexible relation between silver shillings and gold sovereigns until the gold pound, largely a hoarding coin, was introduced.
Spain. Everything revolved around the silver 8 reales (peso), the world's standard trading coin and Spain's best way to convert the riches of its South American colonies into wealth. Copper was revalued regularly and the coins remained in circulation counterstamped. Gold fluctuated against silver.
US. Silver and gold were both political footballs with the silver adjusted by weight or alloy (arrows at date) and the gold not being adjusted much. As a result, there was scarcity of gold in some periods, of silver in other periods (Gresham!). Copper was heavily overvalued and thought of as a service of the government. Supply tended to collapse in times of war.
My guess is that the situation in Ahmedabad was most like the Chinese system with (crucial difference!) copper coins much closer to full weight, so their weight had to be adjusted to volatile market prices more often. Worldwide, there was a large copper surplus but war required a lot of copper, if only for making cannons and cannon balls. I would therefore expect that in times when seaborne trade was flourishing and piracy suppressed, copper would be cheap and in times of war and rebellion copper would be expensive.
Peter
