To recap: I made this claim:

>> "regulated" as used in the founding documents was basically synonymous with "ordered" or "organized". It's the opposite of "dysfunctional" or "chaotic", but it doesn't imply any particular authority structure.

With reference to the first part of my comment (above), I'm going to treat Samuel Johnson's dictionary as having conclusively established that this claim is correct in a general sense; "regulated" bears exactly this meaning some of the time. The dictionary, however, isn't really able to speak to the question of "what does the word mean as it's used in the founding documents?".

You have made this counterclaim:

> A plain reading of the US Constitution[3] paying close attention to the use of "regulate" plainly contradicts this interpretation of the word.

I say that this is false. There are three uses of the word "regulate" in the linked text of the Constitution:

> The Congress shall have Power [...] To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;

> The Congress shall have Power [...] To coin Money, regulate the Value thereof, of and foreign Coin, and fix the Standard of Weights and Measures;

> A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

There is only one use of "regulated". It is open to interpretation whether it is simply a participial form of "regulate" or whether it has developed a special sense.

Let's look at some other founding documents:

https://founders.archives.gov/documents/Washington/03-08-02-... is a letter from George Washington, in which he complains about the "irregular and disjointed State of the Militia", and states that the solution should be "a well regulated Militia law". In this letter, we can note the following aspects of usage:

1. A "well regulated Militia" is the opposite of an "irregular and disjointed Militia".

2. The effect of a "well regulated Militia law" is to "reduce [the Militia] to some order". "Order" is of course, as we learned from Samuel Johnson, synonymous with "regulation", so this is an unsurprising usage. But George Washington's use of synonyms lets us be fairly precise about what he means - his meaning lies in the space indicated by all of his synonymous words.

3. The specific method by which the militia should become "well regulated" is not to impose any additional rules on the militia, but to provide it with "good Officers" who would set a better example than the current officers, and "protect, instead of distressing the Inhabitants [of the province]".

https://quod.lib.umich.edu/e/evans/N25292.0001.001/1:2?rgn=d... is a speech from 1798, after the Bill of Rights had been written, in which George Clinton nevertheless helps us understand the contemporary meaning of the second amendment by referring to it with a synonym rather than a direct quotation:

> THE means of national defence should rest in the body of the people. A well organized militia is the only safe bulwark of a free people, competent on all occasions to repel invasion and suppress insurrection. Standing armies are not only expensive but dangerous to the liberties of the state. In republics every citizen should be a soldier.

It seems likely that George Clinton understood "a well regulated militia" to mean "a well organized militia", since he used those exact words to refer to the concept.

So no, I can't conclude that a close reading of the Constitution leads to the inescapable conclusion that "regulated" as used in the Constitution cannot be interpreted as meaning "ordered" or "organized"; the opposite is true.