Substantially less than 100%. The terms are not synonymous.
they certainly do provide insight into the language used in the constitution, as well as the intent of the authors.
Some of the authors. If it was sufficiently representative, it would have made it into the Constitution itself.
If Congress chooses to discuss a term used in the constitution, their usage does not alter the constitutional meaning, but only establishes a legislative meaning.
This still does not establish the constitutional meaning. You have notably not provided sufficient evidence to establish a constitutional meaning.
the states accepted and enacted the constitution in the context of the papers.
Correct. The states accepted and ratified the Constitution, not the Federalist Papers.
and have no problem whatsoever considering the disciplined portion to be unambiguously a part of the Militia.
That portion being the “whole nation”.
The “whole nation” is not disciplined. I was quite specific: if, and only if, the “whole nation” is disciplined, it is appropriate to consider the “whole nation” to be synonymous with the Militia.
What if I argue that Congress found a different way to ensure the population was “properly armed and equipped” that didn’t require annual assembly?
“Properly” being the functional term here. “Armed and equipped” is not the same as “Properly armed and equipped”.
If you don’t like being held to pedantry, don’t make flippant categorical equivalences of precise legal language.