Could we apply a zero money growth regime to the American economy using the Pilgrim's money supply?
Absolutely. If America was the only economy in the world, then this is exactly the way it would work.
Now if America were to trade with other economies, then your micro observations need to be expanded to include the reality of a world economy.
I think giving yourself an education in economics would be a big help. It certainly would be tedious giving you years of education, one post at a time.
On the gold standard, nations which ran current account deficits or surplus balance their accounts by exchanging gold.
If the pilgrims were industrious, European nations and others would have needed to transfer gold to their economy. Economies ended up with gold bricks, even if they had no gold deposits. In practice, much of the gold remained in New York, London, and Switzerland while the nations exchanged receipts.
But the discipline remained. Run out of gold bricks and you can't import, or you can devalue your currency against gold - which hardly inspires the confidence of your citizens or anyone considering doing business with you.
Remember, the purpose of the gold price was to make gold mining marginally profitable. Its an ideal commodity. It has few commercial uses, so using it as discipline doesn't interfere with industry in any significant way. It just stands there, a raucous fact, as solid as bacon.
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