I believe you're missing the salient point. In the case of the nations you mention, they all had pre-existing industries devoted to the exploitation of nitre, using different methods, and they all had large standing armies to boot. The United States, circa 1861, had neither of those things. Even by the time the Union got 400,000 men under arms they had to import (n some cases hundreds of) thousands of tons of salt petre, weapons, iron, steel and lead. I can point to numerous primary sources which point out the Union could not provide enough of these items in 1861-63 itself and so had to rely on foreign imports. The ability to do this in war time would be expensive, time consuming, and would be brutal on the economy, while providing inferior product to what would be available on the market.
Even Du Pont's best work only got 50 tons a month, which was only a quarter of what was needed. Maybe you could triple that with time, but that even relied on importing the basic product from Britain. Refining good product takes time and its not a simple matter of just combining poop and having it blow up either, its a refined chemical process which got better over time, and the Union was distinctly behind the ball compared to its European peers in the refinement department.
The issue comes down to time, and realistically that's a luxury in a foreign intervention scenario. The prospect of getting off foreign dependence was slim, and the people at the time knew it. I'm not sure how much more that can be stressed.