I doubt any of those letters will have anything to do with the James McClure case for one simple reason: all of them are dated from 1813 or later.
General Armstrong ceased being our ambassador to France as of September of 1810; his next posting afterward was as James Madison’s Secretary of War from 1813 to 1814 (which I’m sure all of these letters relate to).
The matter of James McClure’s claims of American citizenship whilst being imprisoned in France ceased to be within Armstrong’s purview after 1810; in like manner, it wouldn’t have been a military matter that would have merited a response or opinion from Armstrong whilst he was head of the U.S. War Department.
In other words, "These are not the droids you are looking for."
140 Letters (text) - Armstrong to Madison
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213 Letters (text) - Madison to Armstrong