Late to the party again. Maybe someone else has already commented about this but I am impelled to comment before reading further.
Your statement about the dollar is simply not correct. The Coinage Act of 1792 set out to codify what a US Dollar would be. People then obviously knew what a dollar was as the word is used twice in the Constitution (just as people knew what a year was). It was one of those Spanish silver coins. So the Coinage Act had the US collect a reasonable sample of these dollars and then determine the average content of fine silver in a single dollar. This turned out to be 371.25 grains and this became the definition of a US Dollar. So far as I know this definition has never changed. (Federal Reserve Notes are merely denominated in dollars; and quantities of gold were eagles, not dollars.) The single best review of this, IMHO, is Vieira's Pieces of Eight. The link takes you to the 1984 edition which was a single volume. Dr. Vieira has since expanded his work to two volumes, but I have not seen the expanded edition.
ML/NJ
Hamilton had assumed the state debts by rolling them into a national debt with the intention of creating ballast, but also giving full value to all those Continentals. He was accused at the time of doing this to favor speculators over veterans who had held their Continental money, and there were even suggestions that speculators not be able to use their Continentals. Madison killed that amendment in the House.
But were there enough dollars (silver) and eagles (gold) to back those Continentals and the consolidated national debt that Hamilton created? Logic tells me not because we didn't have a domestic supply of gold until the 1820's when gold strikes were made on Cherokee land in North Carolina and Georgia. (We all know how that ended.) The Coinage Act sucked up all those foreign coins for the Mint where they became dollars, eagles and sub-units of those coins. But in 1792, did we have enough gold and silver to back our bonds and Continentals?
Maybe I'm missing something.