I had a similar idea a while back with dye, but rather then making fine/dyed cloth, I came up with the concept of complimentary goods, were selling one good raises the rpice of another.
Civilization A exports equal amount of Cloth and Cigars. After a while, both the Cloth and the Cigarsdrop down 4 gold in price. Due to the surplus of Cloth and Cigars, the prices for Dye and Coffee each raise by 1 gold. However, Civilization A has no way to profit on this, and continues exporting Cloth and Cigars at reduced prices.
Civilization B exports Cloth and Dye. After a while, both goods also drop in price. However, because both complimentary goods are supplied, they drop by only 3 gold, allowing Civilization B to profit off of the increase in demand resulting from their products.
This system would work for each resource in existence, possibly as follows:
Indigo(or Cochineal) -> Dye
Cocoa -> Chocolate
Coffee Beans -> Coffee
Coffee <-> Cigars
Dye <-> Cloth
Chocolate <-> Rum
Not sure what would be done for Fur, but that's sort of always been a second to the other three resources anyway.